We were in WDW last summer the week before AND the week after July 4th. The only major extremely bad crowding was on the Fourth of July itself. It was wall to wall people. We were in Magic Kingdom and it was so packed we could barely walk. So we went over to EPCOT thinking it wouldnt be as bad, but it was worse, maybe because its a smaller park. But the days before and the days after were not bad at all, just the regular summer crowd. I was told that many locals go to the parks just for the day on Fourth of July.
In 2001, we were at Universal at the same times in July, and it was the same thing.