If you're talking about light GA
aircraft, it probably varies from pilot to pilot.
At the rotate speed, it can be quite sharp, perhaps 5-10 degrees per second or more for a short field takeoff.
During flight it would be bad practice not to mention uncomfortable to passengers to move any control surface faster than a few degrees per second and during flight it is unlikely any surface would need to move more than a few degrees in total.
At the flare for landing, I would estimate it's about 2-3 deg/sec for a normal landing. Of course it all depends on pilot skill and how well the landing was judged.
It's all just guess work because aircraft that small are unlikely to have anything to measure/record a parameter like elevator deflection rate.