Me too or mine too

You should answer by "mine too".

Whenever the statement you're agreeing with is a possessive one "my favorite ..." or "my dog always ..." you should use "mine too".

"Me too" is an informal (some grammar fanatics would label it ungrammatical) version of "I too". These are used for agreeing with statements that aren't possessive and say something about the person saying them: Person A: "I received a nonsensical text from John last night." Person B: "Me/I too!" (meaning: "I too received ...")

Hope you find this helpful.