It is hard to know what "significantly more air" means to you. On my saxophone, it does take more air to play A#/Bb with the second fingering, but I would not call it significant. So, if it is that much harder to play the 2nd fingering, I would suggest bringing your saxophone to the shop to see if anything is wrong with it.
That being said, the 2nd fingering has two open holes before the 2nd finger is put down, while in the first the first two holes are both closed. It is harder to push air past the open holes.
I cannot remember the last time I played the 2nd fingering. The first is preferable in almost every situation.