To put it simply, as long as you have a Vgs voltage that doesn't go over the rated voltage for that specific device then the more current you can give the faster the mosfet will switch on but usually it's the other way around and we use a gate resistor to limit the current drawn from the driver so that we don't overload the driver (unless it is a high current driver in which case you will not need a gate resistor).
Alex
---------- Post added at 17:00 ---------- Previous post was at 16:04 ----------
Also note that in a mosfet once the gate capacitor is charged the gate doesn't pull current any more (until you switch off the mosfet).
Once the mosfet is conducting , when you want to turn it off you need to discharged the gate capacitor, the faster you discharge it the faster it will turn off.
In simple switch application you may just stop driving the gate but when you are using a frequency of say 50Khz and you care about the speed you have to use a push pull circuit to give or pull current fast.
In addition when a mosfet is neither on or off and is in the between stage it gets hot because of the current multiplied with the voltage drop across the source-drain, when it is off you have no current and when it s on you have very small voltage drop (because of low on resistance).
Alex