I guess it depends on the handicap, but if you're talking non ambulatory, I'd say neither is exceptionally "friendly". Perhaps BB has a bit less sand than TL. I honestly don't see too many wheelchairs and the like in either of them.
As for kid friendly, they both are. BB has a more organized area, two of them actually. Tikes Peak is for really little ones and Ski Patrol for ages roughly 4-11. TL has a kids area too, but it doesn't offer quite as much.
They are both fabulous parks, you'll enjoy either of them.