Just my opinion, but I would definitely choose March over June. Your spring break is way before Easter. Easter is April 20 in 2014. We have gone during the 3rd week in March a few times. If you plan your days right, the crowds are not that bad and the weather is great. If you are coming from the North, it's a wonderful break from the yucky late winter/early spring weather.
You can go to the parks early before they are too crowded and then take a swim break in the afternoons. If you go in June, I would definitely do this then too. It will be crowded in June too AND HOT and HUMID. By June, you also have an afternoon thundershower to contend with. Much less likely in March.