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I don't know where you're departing from and where you're going, but the vast majority of flights from eastern USA to Europe are overnights, arriving in European cities in early to mid-morning.
I don't really like arriving early in the morning and not being able to check into my hotel. However night flights don't require you to lose a day of your vacation traveling like a daytime flight would. I'm not sure about price differences.
Shane: We take night flights to Europe almost exclusively. For us, it is a good use of time (gain that extra day touring). Also, and most importantly, I have a better chance of getting some sleep on a night flight. Makes the time go by.