twerppoet
iPad Fan
I wish I could be as confident as twerppoet but I honestly can't. The thing is the iPad 3 is an underpowered device, it's CPU is too weak to handle all the scaling a retina display requires and iOS 7 has raised the bar a couple of notches.
I'm pretty sure that things will be better with incoming OS updates as well as app updates (I suspect some of the non-fully-iOS7-ready apps are responsible for the stuttering when it comes to app-switching) but still I seriously doubt it will be as smooth as before. I hope they prove me wrong.
Enviado desde mi iPad con Tapatalk HD
My iPad is a 3. It is working well enough that I'd be hard pressed to tell if it was slower. It may be necessary for you to do a clean install of iOS. Sometimes this is necessary. Not everything is cleared with a new install, especially an OTA (Over The Air) install.
Before you do that though, I recommend a Reset All Settings from the Settings > General > Reset menu. This will not erase things, but if there were any settings glitches that resulted from the upgrade this will clear them out. A few people found it to help after iOS 6 when they had similar problems.
I did have some minor issues and lag right after the install. A restart cleared most of it, and the rest cleared itself by the end of the day. That last I'm figuring had to do with the system being busy indexing spotlight search. Another member (excuse my poor memory) pointed out that the new Photos organization also takes time. There may be other behind the scenes optimization going on as well.
If any of that got stuck for some reason, say one of the databases got corrupted and put things in a loop, the lag might never go away without a clean install.
All I can say, in the end, is keep trying. It is possible to have a good install of iOS 7 on an iPad 3.
If you got Apple Care plus for your iPad (I did) it might still be active. You could think of it as chance to get your money's worth.