There are sections of the country where kids start school in early-mid August and get out by mid-May. So that wouldn't really tweak my decision either way.
I have been to WDW in May and June. I much prefer May. Here's why:
~Weather - warm, but not generally unbearable.
~Flower & Garden Festival - nice thing to have a special event when you are there.
~ Star Wars Weekends (if they are continuing) start in May
I have been in June twice. Both times, it's been very hot and humid. I am from MN. I don't do hot AND humid well. We came over June 7 once for my DH's b-day and it was ok. We were just there June 22-27 because I had earned a trip for free and those were the dates (no choice). NEVER AGAIN! I will take the money before I take the trip if my company does this in June again. It was so hot and humid...ick ick ick. And the crowds were evident. It wasn't wall to wall people but wait times were long a lot earlier in the day than I expected, even Fast Pass returns were a little ridiculous in my opinion.
If you can swing May...take it.