This is a matter of personal choice, you should probably go to the allearsnet.com or the Disney web site and check each one out. Both are great, but for different reasons. I love TL because of the wave pool, and the fact that I hate snow. It doesn't matter if it's fake, like at BB, I don't like going there and seeing snow.
Other than that, people here will probably split their opinions 50-50 for both. For the first week of June, I suggest you get there early, because it will be crowded. The only thing that might save you is that some schools, especially up North, might not be out by then. Our district gets out June 10.
both parks are beautifully themed, BB has more slides and a family raft ride. TL's wave pool has 6 foot waves, and Crush'nGusher, a water slide/roller coaster.