It could easily be a little of both. Different people have different expectations and perceptions of how well an interface is working. It's also possible your iPad is acting worse. As much as we would like it to be, no two iPads are identical, and it's always possible that your unique setup is not responding as well to iOS 9 as others.
The most obviously culprits are other apps, and how much storage you have left on the device. Other apps sometimes have background tasks that run a lot (FaceBooks a big culprit). Less than 1 GB of storage can cause a lot of resource switching, and slow things down.
Even if those are good, there are always settings combinations that can cause unexpected results, minor errors in the actual iOS system files or a small section of RAM that is unreliable and causing mini-crashes that recover in the background, and of course, you iPad could be cursed by Murphy. Sacrificing a chicken may or may not help. (a joke, not a suggestion promoting animal sacrifice).
You can try re-installing iOS 9 using iTunes and a computer. Even if this is the method you used the first time, it's possible it might work better a second time.
Good luck.
P.S. There are reports on the internet that other's, especially iPad 2 owners, are having problems. This is, unfortunately, expected. There are always some problems with an update, no matter what platform you are on. However the number of issues seem to be less frequent and malign than in the last couple of years. Probably because this update was less ambitions feature wise, and concentrated a lot on under the hood improvements and reliability.
Of course, it's far to early to be certain that serious and widespread problems won't crop up. The cautious user should probably wait for the first or second 9.x.x update; especially if they have older devices.
