It all depends on what type of motor is in the tool and some other details.
Induction motors, used on compressors, fans, etc., run in sync with the supply frequency, so rpm is a function of the number of poles in the stator windings and the supply frequency. Voltage does not affect rpm, except in that a 120v 60 hz motor connected across Europes' standard 230v 50hz may rapidly lose smoke!
Universal or 'brush' motors are used in drills and other hand tools to provide more power per lb weight, at the expense of more noise. The rpm of this type of motor is controlled by the voltage, as the motors are generally shunt wound. Back emf in the windings controls the speed. The 'universal' part of the name stems from the fact that many of these motors will actually run on a dc supply. Correct voltage is again vital to avoid possible destruction of the windings.
Cordless tools need charging. The difference between 50 and 60hz on a charger should be minimal, provided the voltages are near matched.
In Britain, all pro builders have to use 110v 50hz on site, and so they use transformers to obtain this from the mains supply at 230v. These are readily available, buy/hire, and a 120v 60hz US tool would be quite happy on this, if a little underpowered/slow.
Finally we need to consider electronic speed controls fitted to tools like drills, routers, sanders etc.. The frequency change may affect these controllers to an extent, depending on the actual electronics design.
Wood work but can't!