The main difference, besides the theming, is that the wave pool at Typhoon Lagoon is much more intense than the one at BB. Every 90 seconds, it generates a 6 foot wave that knocks everyone off their feet. If you prefer a more sedate experience, the wave pool at BB has very gentle waves.
If you go in the wave pool at TL with young children, you could stay with them in the shallow end, where the waves have lost most of their strength. Also, I would have them wear tee shirts in the pool. I've heard of kids being knocked down and getting scratches from the floor of the wave pool.
Both parks have identical lazy rivers, and fast and fun water slides.