for high power subwoofers it is possible to benefit from a thicker cable as those do draw quite a few amps. technically the signal would suffer amplitude losses and thus volume. as for more bass you can adjust the balance of the receiver.
If you aren't putting a lot of power to your speakers thicker wire won't really do anything unless what you're using is tiny. It takes a lot of power to get even a small increase in volume. If you want more bass, the first step is making sure your sub is placed correctly. Put the subwoofer where you usually sit and play music and crawl around the room. Wherever it sounds best to you, put the sub there. If you put your sub in a corner it usually gives it a lot of oomph, but at the cost of sound quality usually.
When people ask about subwoofer cable thickness, this customary says you are sending major power to a PASSIVE sub. An active sub, you are sending it line-level signal, 1 (one) volts peak-to-peak, that's it! I say 24Ga is fine, unless you are running like 100 ft, then I'd bump it up to 18Ga.