I love to hunt Deer every day im alowed. My favorite is during the rut when the Bucks are pumped up and runnig around.

By the time gun season comes 'round the deer are usually 1-2 weeks from full rut peak so we hunt em any time we can

I voted for pre-rut. Technically I hunt all of the above...but I always try and take the first week of deer season as vacation and that's when my real hunting is done. Everything else is just on Saturdays. Usually that coincides with the pre-rut.

I take some time off and hunt both pre rut and rut.
The prerut gives you an opportunity at prescouted and located home ranges of individual bucks. They are cruising their areas looking for the early doe.
The rut changes everything. Now is when the big buck living 2 miles away might chase a hot doe by your stand. So, it also is a prime time to be in the woods.
If I had to pick one time over the other then it would be the full rut. Because now caution is often thrown to the wind and the old smart ones will come out after a hot doe.