Why does my Samsung Galaxy S3 with 4.3 run so slow?
This is because of the update not being done on a clean install. Also Samsung phones have TouchWiz overlay on android which is a bit heavy.

To make your phone fast do a full factory reset after taking a full data backup so that you can restore everything! Doing this would clean up any mess left behind by the update process.
Always try and do a clean install for a major update.