s3 Update Errors and System Modified

So everthing seems to be running great with it now with the exception of since it finally update to JB and whatever else, the phone seems slow.
There is not a lot of apps running, less then prior.
There is a noticable amount of lag when performing certain tasks. Such as switching from home screen to say the phones dial pad or phone log. Going in to certain apps and also functions on the phone.
If anything should it not be faster?

Im going to go read around and see if I can find a solution. Hopefully it isnt a big one or has nothing to do with all of what was done.

Thanks again guys