Should I upgrade PPSSPP?

[LunaMoo]

Both saves and savestates actually improved in new versions, but one of the fixes does happen to cause a problem when old in-game saves made in ppsspp cannot be loaded for example in games from God Eater series which is what you might heard(/read).
It's very easy to fix through, so don't worry, just have to enter settings->system, there disable "Respect FPU rounding (disable for old GEB saves)", and your old save from such game should load fine. Then while still in-game you can just re-enable that option and save your game again to overwrite old "bugged" save with a new "fixed" one.

You want to keep that option enabled especially if you care about cross compatibility with psp as it did fixed it for a few games. Many games work just fine by copying saves between the psp<->ppsspp, however, there might still be some games which saves aren't cross compatible, you can find a list of them in here that's also a place where you could report ones you find which still doesn't work on latest versions from buildbot.