advantages using fsk over ask
The question is not well put, in my opinion;
what I would say is: in a TX-RX link budget suppose you have TX power at 0 dBm and RX sensitivity at -100 dBm. This will cover a certain distance in LOS (line of sight) at a certain RF freq that does not depend on modulation.
FSK has advantages respect to ASK because it is less difficult to implement (or it may need less current consumption). But this is only a general statement, it depends on the cost of the solution, the numbers of channels the kind of application and so on.
Historically FSK (with its derivatives, GFSK, MSK..) comes after ASK and now is widely used for short range communications or low data rate systems, ASK is still proposed in RFIC moslty for legacy reasons.
I hope it can help.
Mazz