We were at The World 4/10-4/18. We were very nervous about this, as we had never been at peak time before, but we had a great time and would not hesitate to go back again at this time.
We never waited more than about 20 minutes for any ride. If you got to the parks right at opening, and used fastpass, you could do what you wanted. The only difference from our off-season trips is that we did not do as many back-to-back rides, although managing fastpass carefully allowed a few.
In the early mornings, we hit the E-tickets right away, and made sure we always got a new fastpass as soon as possible. As things got crowded, we headed to less popular attractions, like Enchanted Tiki Room. We left the parks by about 1 pm each day, having done pretty much everything we wanted. We did 1 late night at MGM (after seeing the early Fantasmic). Didn't try TT or RnR, but Star Tours and Muppets were walk-ons. Unfortunately, not much else was open at that hour.
At MK, we returned to the park in the late evening 3 times. Everything was still packed through the 1st Spectromagic. By the time of the Fireworks, at 10, lines started to thin out and we had short waits for Splash and Big Thunder. After the 2nd Spectro (11pm) most things were near walk-ons. I think we waited about 10 minutes for Space Mountain at that point.
When we checked into Animal Kingdom Lodge, the bellman told us the resort was way below capacity. We didn't have any trouble getting into the restaurants we wanted. Even if no PS were available, we could get tables without waiting too long.