We went in mid May 2009, which was a slightly unusual time -- the birthday promotion was pushing people into getting APs and the park had not yet begun to adjust to the crowds.
That said, we found the parks to be shockingly crowded given that most schools had not yet let out. Just before our trip DLR extended the closing hours for the parks but it did not help much, because they were not really operating at the level they needed. It wasn't like summertime where the crowds also bring extra entertainment, added ride capacity, and so forth. It was like they were ready for slow days and tacked on an hour at the end of the day without doing anything else.
That led to weird situations waiting in line longer to buy a bottle of water than to ride POTC, and longer lines in the morning than in the afternoons. It was often very difficult to find a place to sit down and eat a meal. Heck, we waited almost an hour at the ticket booths because so few of them were open.
After that experience, I have come to believe that summer days where the crowds are even bigger might be better than May because at least the parks are ready to handle the crowds. Things may have changed since 2009, though, so YMMV.