I've seen just the opposite on my iPad Air. Animations of opening and closing apps is quicker and Safari seems more snappy.
First thing to try is to reset your device. Press and hold the Home and Sleep buttons simultaneously until the Apple logo appears. Let go of the buttons and let the device restart. See if that fixes your problem.
Second make sure you have enough free space. With iOS 7 it is recommended that you have 15-20% of the storage space on the device free. For a 16 GB device that is 2.4-3.2 GB free. For a 32 GB device that is 4.8-6.4 GB free. For a 64 GB device that is 9.6-12.8 GB free.
Also check your Settings > General > Accessibility to make sure Reduce Motion is not on.