My first (and only) experience with kayak fishing is on my Hobie, so my perspective is not quite as broad as others that have posted, but I think there are a couple of new ideas I can put forward:
1. First, I think the primary benefit of any Hobie mirage-powered yak is the distance/endurance factor that many people have already mentioned. I used to do a lot of cycling, so I have decent leg muscles, but I think any average person will find that they will be able to cover much more water over a greater time period in a Hobie than in a similar paddle yak.
2. Which model to get? I have an Outfitter, which is the tandem version of the Outback. Yes, these things are TANKS. I fish with a guy that uses a Cobra touring kayak and his kayak easily weighs 1/2 what mine weighs. However, I can actually STAND UP while fishing and move around on deck. The other day, he tried to turn around in his seat and adjust his rods, and flipped. His yak is fast and light, but not very stable. I chose the Outfitter over the Outback because I have kids and wanted to take them out on occasion, which I do. But I have come to really love the open deck space in front of me for storing all my junk. I could easily put a 50# fish up there and my ride would actually IMPROVE since the hull is designed to carry a passenger up there. Normally I carry either a 6" ABS pipe filled with lead as ballast, or I fill a cooler or dry bag with water. The latter is handy if targeting large species of fish, cause the water can be drained off to offset the weight of the fish.
3. Surf entry/exits - yup, much trickier in a Hobie. This is probably the biggest downside, but I am used to it now. We frequently launch at a spot that has a very steep bottom contour and even a small swell will produce rapid successions of 2-4' breakers that peak very quickly and very inconsistent (i.e. hard to read) sets within 100' of shore. My technique for dealing with these is to actually remove the mirage drive and install the plastic plug, lash the drive down to my fore deck with a bungee (along with my other gear) and then I hand-lead the yak about up to my waist in the water, then quickly jump onto my knees, positioned forward of the regular seating position. I can then paddle like Hell to get up over the surf, and I have had a few hairy moments (like most of us). The flotation of the Hobie is excellent, but there is also a lot of drag due to the wide beam - this results in a very predictable (stable) ride, but you really have to be able to put in some short bursts of paddling power to get outside the breakers at times, particularly if you make it 1/2 way up the face of a breaking wave and the suction is pulling you back down
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Exiting the surf is also tricky, but is basically the reverse of the procedure I already outlined. You MUST be more adept at it, as the Hobie is a lot less forgiving of mistakes. For example, you cannot surf waves in the Hobie, IMO. Because of the wide beam and very high primary stability, you cannot lean on a rocker and turn on the wave - you will find that you just get sucked sideways and roll every time unless you hit the beach first. The trick I have found most helpful is to really focus on timing the exit with the swells. Picking the last "large" wave of a set, I will back-paddle to let it roll under me just outside the break, then I will paddle madly to stay on its back and ride *behind* it to the beach. This way I am not fighting the counter-wave that will precede the next wave, but I'm also not trying to get in front of the wave early and surf it (which usually won't work). Timing is key using this method - it is like a ballet of looking over your shoulder at the incoming swells and trying to pick the right wave and through a combination of forward and back paddling, to get right on its hump as it begins to break. When done right, it is a very smooth and elegant landing. The biggest danger, as I said, is getting too far in front of the wave.
I don't think I would attempt landing in big surf on a Hobie (e.g. 4-6 foot or bigger) unless I was able to easily ditch and let it just roll in to the beach while I body-surf. :-) (you can stow rods inside the deck on an Outfitter, by the way, using the rear-most hatch. It is more complicated when you have wiring and a transducer in the way, though.
3. As far as seating comfort is concerned, I find that the Hobie seat leaves a lot to be desired after about 4 hours, but my lower back is helped a lot by cinching the seat forward snugly so that I maintain an upright position. The trick is to get the seat-to-pedal distance set up properly for your leg length - just like on a bike, if you have it wrong, it can be a lot more uncomfortable than if it is properly adjusted.
4. Another plus of the Hobie is the ability to easily fit a sail kit. I love being able to bring a furled up sail lashed to one side of my yak, and then after a full day of fishing I can hoist the sail and more or less ride the afternoon wind back to the launch spot at about 3 mph in our typical 15 knot afternoon winds.
5. Other issues to consider - If you frequently fish in and around kelp beds, the Hobie Mirage drive is a PITA. This is why I bring the plastic plug - I use the Mirage system for surface transit, then remove and stow it, install the plug, and then lift the rudder and spend most of the day paddling around the kelp. It works just fine, and I maintain my paddling muscles for the surf launches. :-)
6. All that being said, I also plan to buy a sleeker paddle kayak for non-fishing (or less "expedition" oriented fishing) activities. As many people have said, there is something special about dipping a paddle in the water and gliding along, which is definitely not the experience with a Hobie. But for an expedition where you are carrying 80 pound of stuff with you (including maybe a live well) and you want to cover 5 or 10 miles in a day of fishing, I think the Hobie is a great choice!