Several criteria should be watched closely when you want to buy a printer of photo quality. I would mainly name the number of cartridges and the ink quality. The number of cartridges will especially play a role in the quality of blacks and whites and the type of ink on the durability of your prints. Let's see that in details now...
The first ones are cheap to make but don't resist well to light. The second ones are made from pigments and are especially resistant to light exposure. Our best masterpieces are printed with these inks.
And on the other hand, photo printers often have more ink cartridges, either to offer a wider gamut, meaning to offer a wider saturated colors pannel hence more relief in the sky and in gradations, and finally, better renderings in black and white. Let's see this in details now...
A - Inks made from coloring agents
These are the inks we use in our office printer or in photo printer under $200. The coloring agents are mixed with water, quite simply. It enables to make especially thin ink drops at the same time (around 1.5 picoliter).
Assets
The ink is cheaper, (although you also overpay for the fact the printer is often cheap.)
Drops are especially thin for thin printing of texts (almost as thin as laser).
It is already possible to make good prints at a reasonable cost.
Drawbacks
Ink doesn't resist to light because coloring agents lose their colors. Prints exposed to light quickly become dull!
It has nothing to do with ink quality, but on coloring agents printers, cartridges always have a low capacity, not compatible with intensive photo prints because you would have to replace empty cartridges all the time.
My opinion and recommendation...
These inks are more suitable for prints that will end up in a photo album, protected from light or when you know you want to change the photo in your living room often!
These inks will also be perfect to make reading prints because the quality of colors can't be questioned once the printer is calibrated.
At the end of 2017, it is safe to say that the life of the Canon and Epson dye inks has made enough progress to keep the original colors long enough for family use. These brands do not hesitate to advance the figure of 100 years when the draw is kept in an album.
Printers using ink made of coloring agents have low capacity cartridges. Not because of a technical problem but for mostly marketing reasons: the printer isn't expensive so the manufacturer earns money on consumables.
With that in mind, I'll also add to play devil's advocate that it also enables to make printers that are less bulky.
B - Inks with pigments...
It is the type of ink to favor when you want to get nice photo prints that will last. Indeed, the coloring agents are encapsulated in a resin bubble extremely resistant to light, instead of being mixed with water. The whole difficulty for manufacturers was to encapsulate this thin powder in a resin bubble thin enough in order to splatter super thin ink drops on our photo prints.
Assets
The ink is very resistant to light - Prints can be certified up to 200 years on certain papers called "museum quality". You can thus guarantee a long lasting if you're selling your prints.
The range of colors - called gamut - is often very wide and anyway broader than the gamut of an office printer. These inks enable to print more saturated colors, especially for printers with more than six cartridges.
It is not due to the quality of ink but printers with pigment-based ink have at least ten ink cartridges for renderings with even more relief in gradations and whites and blacks a lot more neutral and subtle.
Drawbacks
Theoretically few for a photographer!
You sometimes read that the nozzles can get blocked but it depends on many criteria because it is something that never happened in five years on my 7800 Epson.
They're more expensive but mostly because you can buy high-capacity cartridges, so much more convenient!
My purchasing advice
As you'll have understood, you'd really better choose a pigment-based ink printer as Canon or Epson manufactures, especially if you intend to sell your prints. For Canon, the ink will be called LUCIA ® and for Epson, Ultrachrome K3 ® and Ultrachrome HD ®.
C - The number of ink cartridges...
Office printers only need four ink cartridges for the four colors CMYK to work. But photo printers must print colors with a lot more shades and above all, a wide enough gamut or even black and white. No need to go round in circles, it requires more cartridges. Nowadays, Canon sells a PRO printer with 1 to 12 cartridges and cheap printers with ink based on coloring agents have at least six cartridges...
My opinion and my conclusion: it is undeniable that bubble jet photo printers with more than four cartridges offer a way more "photographic" rendering, meaning with more shades. Reliefs and gradations in the sky will be more progressive hence without tone breakings as with an office printer. However, for printers with six cartridges, you'll often have a light cyan and a light magenta. It will be great for color prints, but not for black & whites. For that, you need even more cartridges, especially grey ones. With six cartridges only, black & white prints often have a predominance that is difficult to correct, even with a calibration in due form.
How many cartridges:
6, 8, 10 or 12?
The augmentation of the number of cartridges doesn't have the same use depending on the printers and the brand: some cartridges are used to print more saturated colors, some other additional cartridges only have the effect to get nice rendering in gradations and some others are used to print black and white correctly. Indeed, when a printer must print white, it just has to avoid splattering ink on this area! Logical, but here's the problem: under certain angles, it is visible that the print doesn't have the same reflections where there was ink and where the paper was just left blank. The ink reflections are not the same as the paper's!
And finally, for those able to read a chromaticity diagram, it is undeniable that it is on printers with the biggest number of cartridges that we see the wider gamuts. But not everyone needs to print very saturated colors on a daily basis! My 7800 Epson printer is five years old and I never felt limited by my "tight" sRGB. Even the stained-glass windows of Bourges cathedral couldn't be improved much and only in reds if I changed for a more recent 7900 Epson !
2 - Printing precision: size of the ink drops and printing definition
Two important criteria could be watched to know which printer makes the most accurate prints :
The size of the ink drops (their thinness)
The printing definition (in dpi but not to be mistaken for the definition of your photo!!!).
Size of the ink drops
For a few years, we witnessed a show-off competition between Canon and Epson to know who had the thinnest ink drops. Nowadays, Epson goes first with a thinness of 3.5 picoliters against 4 for Canon (on printers with pigments-based ink) but is it determining?
My purchasing advice
I honestly believe that it is NOT determining so you're free to choose between those two brands. Honestly, I won't be of much help here because my heart is torn between the two of them... I indeed own an Epson 7800 but it is five years old and five years ago, competition was not the same. My next printer could totally be an Epson 7900 as well as a Canon IPF6400 on this criterion only.
And about printing definition, the famous 1,440 x 2,880 dpi...
Canon will offer the standard value of 4,800 x 2,400 dpi and Epson 2,880 x 1,440 dpi. It's about the accuracy of spattering of the ink drops on the paper - which has nothing to do with the dpis of your photo, rather around 200 to 300 dpi. I might as well tell you right away that if I manage to find a difference between the 1,440 x 720 and the 2,880 x 1,440 dpi of my Epson printer, it's only because I find more relief to sky gradations at 2,880 dpi. On details, I don't see any difference, even when I get real close to the sheet.
My recommendation to help you choose
Don't bother comparing these record figures of printing definition. They don't mean anything anymore. Just be aware that marketing services will do all they can to sell us the next 100,000 x 50,000 dpi because when we reach these figures, our eye won't have been able to make a difference for ages! However, when I print a photo with nice gradations, I choose the highest printing definition. Reliefs look even better.
Printing accuracy: Canon = Epson!
3 - Printing size
Another way to distinguish printers is to choose them according to their maximum printing size, or more accurately their maximum printing format: A4, A3, A3+, A2, roll paper for digital printing of your panoramas, etc.
My opinion: what "ideal" format? A3, A2?
If you really buy a printer because a print is a final goal for you, I highly recommend a printer with an A3 format as a minimum. A print of 30x40 cm seems "all right" to me to offer or sell it for instance. You can thus still choose between Canon and Epson.
However, if you're a fan of panoramic format like me, you'd better choose an Epson printer which, for A4 or A3+ printers, enables to print on roll paper.
4 - So... Epson or Canon ?
Honestly, my heart is torn between the two of them... but here's food for thought:
Canon's pros...
Epson's pros...
Printing quality has improved greatly and is now similar to Epson's. 10 or 12 ink cartridges for "photo" printers, Transparent ink Chroma Optimizer to avoid ugly reflections in white parts of the print (not covered by ink).
Cheaper than its competitor, Near fifteen years' experience at the top of photo quality, Ability to print on roll paper (panoramic format for instance).
Canon's cons...
Epson's cons...
More expensive; Impossible to print on roll paper for A4 or A3+ printers.
No transparent ink to fill in the white parts of the print and give them the same reflections as the inked parts.
I'll give you a few additional elements in the next page... per printing size, price categories, ink quality...
Choose pigment-based inks if you favor resistance in time. Only those inks enable to make prints that will last long because their ink is encapsulated in a resin that is very resistant to light. You won't have to hide your prints in your drawers!
Choose inks with coloring agents if you only need reading prints. Prints look just as good but are way less resistant to light.
The number of ink cartridges shouldn't be a determining criterion if you're debating between 10 and 12 cartridges, according to me. On photo printers, you'll always have many cartridges nowadays. Caution with marketing speeches: photo printers print incredibly well for a long time now so they have to find new assets supposed to wash cleaner than clean. It is no casualty that I'm still printing on my "old" Epson 7800 that is five years old... it is the same with drops of 3.5 or 4 picoliters... It is just the same!
However, don't hesitate to choose a printer enabling you to print in 30x40 cm, that is to say in A3 format. It looks better if you want to offer or sell your prints.
EPSON or CANON: I still don't know what to answer now, at early 2018. My heart is torn between the two of them, with a thing for Epson though! But there's really no big difference...
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My opinion and recommendation... 
These inks are more suitable for prints that will end up in a photo album, protected from light or when you know you want to change the photo in your living room often!
It is the type of ink to favor when you want to get nice photo prints that will last. Indeed, the coloring agents are encapsulated in a resin bubble extremely resistant to light, instead of being mixed with water. The whole difficulty for manufacturers was to encapsulate this thin powder in a resin bubble thin enough in order to splatter super thin ink drops on our photo prints.
Office printers only need four ink cartridges for the four colors CMYK to work. But photo printers must print colors with a lot more shades and above all, a wide enough 
How many cartridges:
