If it wasn't so close to Easter, I'd probably go with the end of March. Even though the crowds will be worse, the weather should be much better (we have a late March trip planned for 2017, when Easter is in mid-April).
The way we deal with crowds is to mostly hit the parks from rope drop until about 1 pm, while making a judicious use of FP+ (we typically spend afternoons back at our resort). We also typically buy at least 7 day tickets (which, for example, allows for 3 MK days, 2 EP days, and 1 day at each of AK and HS). We only hit our favorite attractions and rarely do the same popular attraction more than once on the same trip. This allows us to divide the parks into manageable pieces that can easily be conquered within the first 3-4 hours.
To me, the biggest advantage to June over March is better temperature for the water parks (which we love). But this can be at least partially offset by the fact that June tends to have more afternoon thunderstorms. So, even when water parks are factored in, I think late March beats June from a weather perspective.
