Not the voltage ampitude, as that's easily switched by changing the input transformer winding ratio. It also has to do with the input frequency, US is 60 Hz while Europe is 50 Hz.
Any device that uses a synchronous AC motor will run slower. Bought a clock radio in England, worked fine. Rotated back to the states, unpacked household goods plugged clock radio in and set alarm for 06:00. Around 5am the alarm went off and the clock said 6am - OPPS forgot to change the little gear.
Taking say a American Toaster to England and using a transformer to step the 240 down to 120 took about 30 % longer to toast bread.
Some PSUs that state 120/240 50/60 Hz that have a switch to go from the 120->240 while the may work at the reduced 50 Hz, still have to work Harder to provide the regulated DC outputs (due to increased on time for PWM circuits) to compensate . And it may be for this reason that some Computer PSUs (and other US electronics) tend to fail.
Do agree with noidea_77 on just buying a new power cord, should only be a few Euros.
Also concur, should not have to worry about polarity.