Two separate issues
1) frequency and "Volts per Hz" (V/Hz).
2) power level, which is really voltage and current capacity. That comes down to heating.
In SOME cases, the V/Hz is not an issue. 480V 60Hz is equivalent to 400V 50 Hz. No issue.
277V 60 Hz is equivalent to 230V 50Hz, and while the 277 voltage is not in common use for much aside from lights, it is also a good straight equivalence.
240V 60 Hz, is, however, equivalent to only 200V 50Hz, in terms of V/Hz, so that does not work as well, 230V is the common 50Hz voltage.
When the volts/Hz are the same, flux is the same in the core, and heating, etc from the magnetic field will be similar to the 60 Hz case
As for VA, There you have a difference, and it is roughly 5/6, since the same current is allowable, but the voltage is reduced. So by definition, the VA will be reduced for a transformer.
For other items, it depends (You only asked about transformers)
Current dependent items, such as AC solenoids may perform nearly the same, since they do not use resistance, but AC impedance to limit current. (There COULD be an issue with buzzing, depending on the "shading coils" used)
Motor power is less, again because the voltage is less, although the current can be the same. At the lower voltage, the 50Hz motor will have more current capacity to reach the same power that the 60Hz motor reaches at higher voltage. The 60 Hz motor at lower voltage can only operate on the same current as before due to heating, so the input power is reduced.
There COULD be an issue with regard to fan cooling, since the fan is going slower, and the current has not changed. Many motors have reserve capacity in the fan, and will be less affected. Some may have power further limited simply because the fan at 5/6 rpm can only support the heating from a lower current.