iPod Touch 5G Issues

I got my iPod Touch (5th gen) last spring and really liked it as an 'iPhone without the phone'. After the iOS 7 update, battery life has gotten somewhat worse-not unreasonably bad, but noticeably worse. Also, I have seen a lot more lag than I was used to on iOS 6. I know some of this might be down to the older A5 in the iPod Touch, but my friend's 4S on iOS 7 doesn't lag nearly as much as my iPod Touch. Is there anything that I'm not aware of that might be causing the lag or the bad battery life? I've tried using third-party apps like Kingsoft Battery Doctor, but battery life still isn't notably improved.

Note: Storage probably isn't causing the lag-out of 32 GB on the device, I've used a max of 9-10 GBs depending on how many apps and other stuff I have installed.