My iPad2 has become very slow too. And to start off, yes I do a hard restart about once a week, generally close apps after using them, don't leave a bunch of apps running in the background keep iOS updated. I'm up to date but it has been slow even before going to iOS 8.
Mostly what is slow is having links open up in Safari. Doesn't matter if I'm clicking something like an email link or already in Safari and clicking to another page. It is as if I have a slow internet connection but I don't. Pages open quickly on my other devices, I stream movies fine, download speed test usually right around 10m down/5 up.
Is it just Safari that has become the pig? It reminds me of how a Windows computer becomes slow after a couple years of bloat.
Texts go fast, streaming videos play fine, etc.