I know the OP asked about Verizon, but since they also asked about others, here goes. My last two trips to WDW had very different reactions to cell phones. My first of two was with Sprint. I can honestly say I have never had worse reception in my life...pretty much anywhere on property was horrible. I could stand in one place with full bars and then take a 1" step and have no signal. It was horrible.
My last trip I had switched to Nextel and have never had better covereage! I know it helps that there are portable Nextel towers in various locations with all of the construction, but it was great reception.
My two cents...