Turbo raises your power level and makes you move faster and hit harder. A higher PL means a faster moving and harder hitting character. You might not notice it much when you switch turbo on normally, but you notice the jump in speed when you transform. The transformation makes the jump in your PL.
I can notice a substantial difference when playing against bots. I always go one on one with a character that will have more PL to start with. This means I have to EARN my victories. I can garauntee about 95% of the time, if I swoop without having my turbo on (thus, my PL raised) i will not be able to hit the bot. So PL does make a difference. And in later versions when more transforms are added, you will really notice PL increases making the difference.
Maybe you get whooped by new server joiners because they have played longer than you? Either way, your PLs should eventually average out from the balancing effect of ESF.