We have done both several times, and used to live just a few miles from Disney. I personally would choose March, but neither will have low crowds. Your March dates are at the height of spring break. It won't be Christmas like high crowds....but from my experience still crowded. June will likely be almost just as crowded, but significantly HOTTER. The heat/ humidity can really effect some people. If you can't handle as much heat/ humidity then pick March. If that doesn't bother you, then personally I would pick the best month for your schedule or cheaper time. I hope you have a great vacation whichever month you choose!