go to settings. General. Reset. "Reset All Settings"
go to icloud. Turn off documents and data sync if it's on switch it off or vice versa. I don't know why this works. But it does.
Turn off all the crap you don't need. I.e. Background App Refresh. Location Services.
GO to accessibility and turn on Reduce Motion
clean out safari. I.e. Cache etc.
the first two are the most important. And helped me.
Truth be told "The New iPad" was replaced in 1,2,3,4,5,6 months because Apple realized they had a dog on their hands. The GPU can't keep up with the retina display. That's why the 1.4GHZ processor and more powerful GPU in the ipad 4 dances circles around our ipad3 investment.
iOS7 is garbage performance wise they haven't optimized it for older devices. Not yet a little bit with 7.0.3 but iOS 7 is a memory hog.
I Bought the iPad Air it's just too fast and light to resist. It's great but Safari still crashes. I can see under diagnostics that low memory logs are generated by Safari. When will Apple learn to put more ram in a tablet? Sure it runs iOs7 otherwise perfectly but let's see what happens when ios8 or 9 come out. I'm gonna stick to the OS from now on that the device ships with.
ONe one exception to that rule is Macericks which has breathed new life into an otherwise paper weight MacBook Pro 2008.