From what I have heard they are all packed for the 4th of July. Magic Kingdom is by far the most crowded though. Epcot is supposedly not as bad. DHS I would expect to be fairly bad that day as it's a fairly compact park. Animal Kingdom has a lot of open space so maybe it copes better with the crowds.

That's just going off what I saw on here once though, someone else will hopefully come along with first-hand experience.