First of all, you have to compare apples to apples. You don't compare solo kayaks to tandem canoes, you compare them to solo canoes. A lot of people who love kayaks for fishing have never paddled any canoe but a clunky tandem.
Then, you have to differentiate between flatwater and moving water. Flatwater could include large, slow rivers as well as lakes. The biggest problem any angler will have on flatwater is wind, and kayaks do have less "sail" area and so are better in the wind. That's not usually as much of a factor on moving water and smaller rivers.
So...narrowing it down to moving water, anything from very easy to Class II, a solo canoe is, in my opinion, the superior craft. Let's compare them.
1. Speed--"speed" is nice because it includes the ability to paddle upstream against the current, and to get through long, dead pools that usually have poor fishing in order to quickly get to the next good spot. With a double bladed paddle, a decent solo canoe will hold its own with just about any kayak for this. So they are roughly even.
2. Weight--weight is important for transporting to and from the river on a vehicle, loading it on and off the vehicle, and carrying it to and from the water at difficult accesses. Most good solo canoes range from 33 to 45 pounds, while most kayaks are a good 10 pounds heavier. Also, the shape of the canoe makes it easier to tie down (you don't need special kayak carriers) on your rack, and also makes it easier to carry on your shoulders. Advantage canoe.
3. Comfort and ease of getting in and out--a lot of kayaks have comfortable seats these days, but you're still sitting almost like sitting on the floor, with your legs straight out in front. In a canoe, you're sitting more like sitting in a chair. For both, a good backrest is a must, as is good butt padding. Most people who rent canoes end up sitting on a floatation device with no backrest, and hate it by the end of the day. But with some thought and experimentation, you can come up with very comfortable backrest and padding. The other thing to consider is ease of getting in and out. This is probably a wash, since SOT kayaks are easier to step out of and stand up in 1 to 2 feet of water, while canoes are easier in less than a foot of water. In my personal experience, it's pretty easy to find a good spot to get out of either, but when you accidentally run aground in a shallow riffle and HAVE to get out, it's easier in a canoe. Overall...about even.
4. Vantage point--the higher your head is, the more you can see. A related note is that the higher your shoulders are, the better you can cast. While in a number of hybrid craft and some SOTs you can stand up and fish, that's not the smartest thing to do when in strong current. Bump into something and you take a header. In the seated position, you are higher in the canoe. Advantage canoe.
5. Carrying capacity--in my solo canoes, I can carry five fishing rods, rigged and ready to cast, all within easy reach of my hand, and all with tips within and below the gunwales so they can't get snagged on brush or get in the way when I'm battling a big fish. I carry 5 3701 Plano boxes sitting flat in an auto battery box that is strapped beneath my seat, also easy to hand and off the bottom of the canoe where the lures inside will stay dry. When I do overnight trips, I can carry a 4 person tent (I hate being cramped), a thick sleeping pad, a sleeping bag, a cooler big enough for multiple days of food and beverages, cooking gear, and my fishing tackle. No kayak can come close to matching that. Strong advantage to the canoe.
6. Handling--when fishing, I'm constantly making minor positioning and course corrections without laying my fishing rod down. I can do this easily one-handed with a single blade paddle. When I'm not using the paddle, it's lying across my knee with the blade end lying on the gunwale, where drips don't get in the canoe. You simply can't do those kinds of minor positioning strokes with a double blade. Some kayak fishermen use a small one-handed paddle to do them, but that obviously requires carrying an extra piece of equipment, and doesn't have the leverage of a longer single blade. And when they have to set their double blade down, it's a lot more awkward and in the way of their fishing. Advantage canoe.
7. Stability--a number of kayaks and hybrid craft are now more stable than most canoes. You can stand up and fish in them. You can also do so in many solo canoes, but not with the same comfort. I don't consider this a very important consideration, because I'd rather be sitting just because it is more stealthy, but some really like it. Advantage kayak (some of them).
8. Learning curve--it's easier with a double blade, but then again you CAN use a double blade with a solo canoe. But that would negate some of the other advantages of the canoe. On the other hand, you can do MORE once you learn how with the single blade. Slight advantage kayak.
9. Price--on average, kayaks are cheaper than good solo canoes, but many of the newer and more popular kayak models among anglers are as expensive as the better canoes. Slight advantage kayak.
Have I covered it all?