We've been both times, and the first of June is much less crowded than Easter - but don't interpret that to mean it's empty. The crowds in early June are healthy, and you'll still need to arrive early and use FastPass when appropriate, also make sure you have PSs lined up for meals you want other than counter service. The impact of GayDays is that certain parks are indicated as the park for a particular day, so the crowds become much larger at that park. With a little advance knowledge, you can plan your park visits to avoid the larger crowds. And don't forget that GayDays are not an officially sanctioned WDW event, so plan around them if they offend you or if you want to avoid the crowds, but don't blame WDW for them if they impact your vacation!