I think the biggest difference is in the 'touch' of the instrument. You can play anything on your electric that you used to play on your acoustic, but it must be played differently.

Unless your electric guitar has unusually heavy strings on it, you need much less pressure to fret the strings, and your picking action must be almost delicate compared to playing an acoustic.

The reward comes in the form of the expressiveness that results from the subtle response to variations in pick attack, and the lovely sustained tremolo you can achieve with your fretting hand. Enjoy! :)