In my own case, everything was slow. Loading apps, loading web pages, whatever. And the difference after a clean install now is huge. Went back and did the same to an old iPad that I stopped using for its sluggishness, and it's usable again.
Complex devices, so there's certainly going to be a complex set of problems, but I think that some of it is due to us taking Apple's message that iOS devices are appliances to heart, whereas the truth is that these portable computers still need mysterious maintenance rituals. It's been impressive, but Apple's still got some work to do to make these things bulletproof.