BB is 0.18
#4 birdshot is .129
In my opinion birdshot is, at best, questionable as a HD round. Any of the buckshots are a better choice. I use #4 Buck for indoor use for a balance of penetration vs. over-penetration, but that is purely preference. 00 is the typical self-defense round.
Think about how hard it can be to knock down a 1-2 lb cock pheasant with birdshot...