Putty has it exactly right.
In most cases if you are not tripping your 15a breaker, there isn't a whole lot to gain by increasing it to a 20a. The increase in cable gauge, however, would almost certainly help, as it would cut down on circuit resistance.
I have run 10 guage wire to each component to cut resistance, but put in 15 amp breakers to help protect components not expected to draw much current. A 20 amp breaker when not needed is just adding to risk.