We have almost always gone in early June. A few of our trips were mid-June, but probably about 6 or 7 trips were early June. I've never been at Thanksgiving, so I can't make an actual comparison, but we've found early June to be crowded, but certainly do-able. We take advantage of early entries and stay in the parks until noon or so. We come back to the villas for rest and swimming and usually are ready to be back in the parks by 6:00 p.m. We've always been able to do all the rides we wanted using fast passes and having a plan. The hours after June 1st have usually been extended so the MK is usually open a little later. Friends of mine went Thanksgiving week once and said they'd never go again. The wait time was long and it was very crowded. We do so much advance planning. My DH figures out which park is open early/late, checks trends in attendance and makes a plan for us to follow. We think advanced planning makes the trip much better.
HTH