A machine running with brushes only cares about the voltage, speed is adjusted by limiting the width of the AC frequency sine wave. At a lower frequency there would be some slight increase in induction losses causing a slight increase in temperature.
An induction motor would run at a speed controlled by frequency so at a lower frequency it would run slower and heat up a little more with even less fan cooling.
A brushless motor converts the AC power to DC first before it converts the DC to pulses to control the speed, unaffected by frequency but enabling much higher speeds and higher power/efficiency. This is mostly used in battery powered tools as they are DC to start with.
So you can see that in most cases, as long as the voltage is correct, most power tools should run perfectly well on either frequency as long as the 60hz design motor, used on 50hz, is not being pushed to its limits and overheats. The 50hz design, used on 60hz, would in most cases run slightly cooler due to lower losses.
Overheating is very unlikely as most motor designers would build in a tolerance to enable their design to be used worldwide. On a brush motor the frequency label is there so the you don't plug it in to a DC supply. The motor wouldn't care but the speed control wouldn't work and the switch would burn out due to excessive arcing.