Actually, Mike was right. It should be "me." If you use "I," you need to follow it with "am":

Anytime I say "someone is older than I am", I will usually say, "John is 20 years older than I am", as opposed to "John is 20 years older than I". The latter sounds a bit stuffy. It's correct, but (IMO) stuffy.

However, "John is 20 years older than me" isn't correct.