I have two trips planned to WDW in coming months - one 11/4-11/11 and one 4/20-4/27 - at which time do experienced Vero Beach visitors anticipate would have nicer weather?
It may be a little cooler in April, but November there is still the chance of over spill from Hurrican season and at the very least the beach can have been a bit "chewed up" Personnally I'd go for April.
Feb-April are the primetime tourist (and Snowbird) time for Vero Beach. Chances are November willl also be nice weather but April is probably better (I also think there is a substantial point difference so you might want to consider that as well.)