I'm having a similar, but not exactly the same, problem. My 3GS was working fine but started to slow down over the weekend (loading apps, opening, accepting touch commands). It has only recently been updated to the latest OS, but it's taken about 4 weeks since then for this problem to manifest itself, so I'm not sure that's the issue.
Battery life also seems quite fine (at least according to the power bar). Today it has gotten MUCH worse - some apps take forever to open but then do not function, or are ponderously slow. Worse, some apps fail to open at all and just crash.
Thinking I may have too much on it but can't even check this as phone keeps crashing! Any thoughts would be appreciated.