To get more power (for quicker accleration):
If your battery voltage sags during acceleration, replacing it with a better battery that is more capable of delivering the current required for that will help. How much it helps will depend on how much sag there is with the new one vs the old, current required, system voltage, etc. For example, if you had a 72v 100A max-current controller, and your present battery sags say, 10v under max load of 100A, then at nominal voltage of 72v you'd get only 62v x 100A = 6200W out of the battery, while if it had no voltage sag you'd get 72V x 100A = 7200W, or an entire 1000W more. Whether that's enough depends on what it takes to give you the acceleration you're after.
Otherwise, you'd have to (also) change the controller to get more power, since it is what converts battery power to motor power.
If you only change the motor, it's probably not going to give you faster acceleration unless you're willing to live with a proportionally lower speed, because for the same power you can either have more speed or more torque. (higher kV (RPM/Volt) gives lower kT (torque/Volt), and vice-versa)
Generally, just replacing the motor, the things that can change are:
--the speed (if it's a different kV, or different wheel diameter)
--if it's a larger heavier motor it may take longer to overheat if you were having that issue. .
--if it's a wider magnet / stator motor, it might have more torque for the same current (but may run slower)
Other motor characteristics may affect how the controller drives it, and if the controller is an FOC type then it will require reprogramming / setup to configure it for the new motor's characteristics, and possibly tuning it to operate it best.
Your existing motor can probably handle a bit more power especially if it's only a momentary need, for acceleration, and isn't continuously required. (most can) If you need that higher power to maintain a higher speed, it may not be able to do it very long (depends on the motor and the riding conditions).
If you get a larger controller that can supply enough higher phase current than your present controller, and the battery can handle supplying the higher current to the controller to allow this without shutting off or sagging in voltage more, then you should get better acceleration with your present motor.
Note that every motor does have a saturation point at which more phase current just turns into heat instead of increasing torque, but that point is not usually documented and would have to be tested to find out where it is.
