We were just there June 3 - 18, and didn't really notice a big difference in the crowds in the two weeks. As the previous poster said - you have to go with a plan (albeit a flexible plan); and we like to get up early, go back for a mid-day break, and then go back to the parks at night. We used fast passes a lot! I had at least one ADR a day! We had a great time!!!!!
In the last few years, we've been just about all the weeks in June, the first two weeks of July, and the first week of August. The week around July 4th was crowded; but very do-able and we still saw everything we wanted and had a great time!!
I am considering getting an AP next year, so we'd go in late July, then our Christmas trip, and be able to back in June the following year!! That's my plan - just not sure if its DH's plan too....