Induction is usually heavier for the same power, so if that's a concern, servo gets an advantage there. Depending on the induction motor, you may be able to overspeed it a decent amount. For example, 4-pole Baldor inverter duty motors are rated to run up to 6000 RPM. So that means constant torque up to 1750ish RPM, constant power from 1750 to 2625 RPM (150% rated speed,) and then power drops off as you get to 6000 RPM (not sure how fast.) Those higher RPM's are handy for running smaller tools that can't use all the power anyway.
Some servos also have a max speed that's higher than their rated speed. 3000RPM rated and 5000RPM max are common. So you get some constant power range, but not as high as some induction motors.
With a servo you could add rigid tapping if you use a timing belt as well (if you aren't going to do rigid tapping, use a V or poly-V belt, they run smoother than timing belts.)
Are there any particular models you're looking at?