110V AC/ 9V AC power adapter (America) Vs. 220V AC/ 9V AC power adapter (Europe)
Your 9 V AC will be 9 V AC; the secondary side doesn't know about the primary voltage. So that's no problem. 

What could be important is that in Europe you'll have 50 Hz output, whereas the US adapter will output 60 Hz. (Well, it doesn't make 60 Hz, that's what the mains supplies in the US.) This is not a problem if the device converts it to DC (most likely), but if you would use it for a digital clock that will run 17 % slow if it gets its clock from the mains frequency, and expects 60 Hz.