We went to both on our trip in May. It felt like BB had way more stairs. Not sure that is true, but it felt true. That said, in BB, when you are climbing stairs, you are always going up. In TL, you go up a dozen steps, then back down 3-4, then back up again as you move through the jungle.
They both have lazy rivers, both have tube rides (single, multi & family), both have high speed, straight-drop slides, both have wave pools.
TL has the swimming with the sharks (we skipped this), a cool water "coaster" where you ride a tube and go both up & down, and a few twisty body slides (no mat or tube. The wave pool is INTENSE and pretty rough.
BB has some twisty slides you ride on mats (love these!), a toboggan-type mat slide and the wave pool is more calm.