It "shouldn't" pull enough amps to feel different at all(unless something is binding and or the servo is damaged). Your motor is pulling 30-70 amps, I doubt that servo pulls more than 3 or 4 at most. I bet it was the tires that made it feel different.

For the ESC; even though the new servo is pulling more, the BEC should be adequate. Although I have seen various ESCs have better BECs than others...