I am an avid Kayak Angler and think they outclass float tubes in every possible way, except perhaps if you plan to hike a long ways then fish. I have two Wilderness Systems yaks, a Tarpon 120 (12 foot) and a Ride 135 (13.5 foot). With the Ride, stability is not even a thought. I always stand and fly fish from it. No need for outriggers and all that stuff with a correct hull design for fishing. I'm not comfortable standing in the Tarpon, but many people do. When seated, you would need to try very hard to dump either one. The Tarpon is a quicker, lighter, and faster boat than the Ride and possibly it is a better river yak than the Ride. The Ride is ultra stable, easy to maintain speed when travelling, and a super fishing machine in everything but small streams. I'm a fan of Wilderness Systems, but there are several other purpose-built fishing kayaks which are just as good or better depending on what your expectations are.
Sit On Top models are much more fishing-friendly than Sit In Kayaks in almost every possible way. They are also heavier and generally slower. There are exceptions to every rule.
The FreedomHawk kayaks seem to have a pretty good following, but I don't have any experience with them. IMO the built in outriggers are two more things to break or malfunction.
Fishing specific SOT kayaks are going to be somewhat heavy and that figures into transport. My Ride135 weighs about 80 pounds. I have no trouble putting it on the roof rack of my car even with a wrecked shoulder and ruined back. It is all about technique, doing it correctly, and staying strong enough to get out of your own way. If you will be chucking it in the back of a pickup or putting it on a trailer, then it is no issue at all.
There are no "cons" to kayak fishing in my opinion. You won't be able to do as much open water Great Lakes fishing as folks in regular boats, but that is about it. I fish Lake Erie in my Ride135 several times each year. Got to play the weather and use your head. You will be out in the elements, but proper clothing and common sense solve those issues.
If at all possible, go to a decent paddle shop on one of their demo days and try to paddle as many different kayaks as you can. Kayak fit and usability are very personal things. Nobody can really tell you which one is "best" for you, but you can make some informed decisions.