Yes, all things equal, simple physics,

15 will move more air and go lower than a 12
12 will move more air and go lower than a 10
10 will move more air and go lower than a 8

But now if you take a 15" discount speaker like maybe a inexpensive Behringer, or other off-brand, it will never sounds as good or go as low as a 12 maybe even a 10 of a very hi-quality brand.

Amplifier
Speaker
Cabinent
Design

All these things have a factor also