Look I hate to be pedantic, but I have to be. You said that your correction was "slightly more correct", but it's not. It's only more correct in the situations that I outlined. There are many more situations (not only general conversation, which is the only one that you mentioned) where it is correct. I just don't want any non-native English speakers to get confused by an offhand joke. Now that I have completely killed your joke, can anyone tell me how to change my name to "jokekiller"?

"I" can be used in formal situations. Funsubstance isn't a journal, a business letter, or a dissertation. For this comparison "me" is the perfect option.

"Better than me": "I" is a subject pronoun and "me" is an object pronoun.