They are both ok, but there's a difference in meaning. "We're of the same age" means "We are roughly the same age". "We're the same age" means you are much closer in age than just 'roughly'. "We're the same age" implies a much shorter difference in age - you are the same age or just a couple of years difference. This is a little subjective, of course. Also, "We're of the same age" isn't heard much. More natural (or more common, at least) to say instead, "We're roughly the same age".

Hello Heidi, yes, they are both grammatically correct and the meaning is the same for both sentences. In usage, however, "We're the same age." is much more natural, common and informal than "We're of the same age." Hope that helps.

Heidi, Both would be understood. The first is more modern and the second I would expect to see in older literature. The second could be read as saying that you both come from a similar point in time.