We enjoy them both, BUT, if you're looking for one to try first, I would suggest Typhoon Lagoon. Here's why:
#1: The huge pool area has the single 4 foot wave that comes every few minutes. This is a blast for adults. I find that riding this wave is much more fun than the constant "wave pool" at BB. Actually (and this is just me), the wave pool concept drives me a little nutso. It's so constant, just getting tossed around. I love it at TL when the whoosh sound signals the start of the big wave and everyone screams!
#2: Shark Reef. It's still fascinating to me and I love to go through it several times. You are given mask, snorkel and vest in line (usually very short, if any), then you sit on the edge of a shallow area of seawater in a huge tank full of all kinds of fish. You receive instruction in snorkeling if you need it. You are not allowed to dive down and you must keep moving forward (otherwise you'll get run into by those behind) and you just use your hands to paddle (again so you don't kick those behind you). They have a ton of lifeguards. It's an extremely safe way to snorkle with sea life as if you were in the Caribbean. The sharks look really big (they're only about 3 1/2') and are amazing to watch. Just so you know, there are nine species of hammerhead sharks and these have not teeth and only eat lobster and crab. They have sort of hardened gums instead of teeth...same thing with the other species of leopard shark. There is no danger, just a really cool experience.
#3: Crush N Gusher, the new tube water slide roller coaster that goes UP as well as down. It has conveyor belts to bring you up additional hills. Very fun!
#4: BB has a ski lift to bring you up to the water slides. I have found this line to be gigantic. I like how TL is set up. Like another poster said, most of the other slides are the same. I do think BB has a better kids area but that won't apply to you and your fiance.
#5: The lazy river. I really like the TL lazy river because it is surrounded by the most beautiful flowers and plants and palm trees. I like the theming of docks with boat motors spraying you with water, of surf shops and alligator sneezing on you. I also like going through the dark cave. The lazy river at BB doesn't do it for me. The "melting snow" theme is cute but a little weird. I guess I just enjoy the real plant life instead of the fake snow.
When you're there, buy the refillable mug, get a temporary tattoo of your favorite Disney characters and enjoy!