Let's see....on my Android phone, I had to deal with a horrific lag, after owning it for a few months and getting several updates from HTC and Sprint. Even rooting and installing a custom ROM didn't help. When I woke the phone, it would take anywhere from 15 seconds or more, for the screen to populate, so I could use the phone. The apps I used didn't sync to anything else and also crashed on a regular basis. The keyboard lag, when typing, was awful. Regardless of which one I tried, it would take forever to type anything and I'd often have to reboot my phone to get it to work right again, but that never lasted more than an hour or so. I actually had to reboot it several times a day to keep the phone functioning.
No amount of killing tasks, leaving them alone and letting Android handle it, or any other advice I read helped.
My 4S has already received an update, didn't slow it down and make it lag, at all. I wake the screen and it's there instantly and ready to go. The only app that crashes on me is the Facebook one and I rarely reboot.