I have an old Dave Scadden inflatable kayak that I traded a fly rod for. Its portable and OK for fishing ponds where I don't have to paddle far. It would probably be good for paddling rivers so long as the river did not have any flat water that required heavy paddling, but I never use it on rivers. You have to fish from a seated position, its slow, it tracks like shit, and it is a pain to inflate every time I want to use it. I also have an old two man cataraft, which has not been used in years and I have just been too lazy to sell -- it is also a pain to row and takes way too long to inflate/set up. And I have a SOT fishing kayak. The SOT kayak gets used 99% of the time.
For our waters in Texas, a hard SOT kayak is unquestionably the way to go -- especially one that is stable enough to fish while standing (like a Native, Diablo, or one of the bigger Jackson models). But our rivers have a lot of flat water and relatively minor rapids. Western rivers tend to have more current and more significant rapids, which would make an inflatable much more doable.