We have taken toddlers to both the parks this year and last. While we love TL themeing, and really enjoyed their park, there is a lot of spraying water in the kiddie area that the little ones just don't really love. I find that area more taken over by the 5 to 7 year old boy crowd. Plus the family raft ride dumps alot of water on you from above and bumps you hard into the sides. The wave pool is not suited at all for little people. However, the mini tube ride is fabulous. My kids did that for hours. Plus, we used the "holeless" tube in the lazy river for our little people and it was a real hit.
Honestly, TL was our favorite until we went to BB. Now I agree that the themeing is a bit strange, but oddly fun. The family raft ride is long and a riot. Just swishing sliding fun - no water dumping or bumping. The wave pool is suitable for little people and you can use tubes (my 2 year old son fell asleep in one). The kiddie area is fabulous for infants/toddlers. It is huge, zero enrty, nice slides and managable spraying water, plus fun jumping fountains. The lazy river doesn't have "holeless" tubes, but it was still a hit, we just had to be more vigilant.
Now BB is our favorite - plus I thought it was a bit less crowded. Hopefully that helps. I think you will have an amazing day in either park, so have a great day! Disney does waterparks like no other.