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I have found, for me at least, overall my xbox runs better if i keep mine in power saving mode. Sure you lose like 20ish seconds of boot up time, and the ability to say "xbox on," but overall i think it is worth it to just keep it in power saving mode. From what i have seen, although i could be wrong, in instant on mode the xbox does a terrible job of clearing out the cache and the UI becomes a little less responsive.
If you ever run into real problems with apps running/errors just hold down the power button, while the xbox is on, for like 10 seconds or so and it will clear it. Plus i treat mine like a PC and close every app when i am done with it instead of leaving it running in the background.