Some do, some don't. True idents who grow up together, exposed to the same people, experiences, etc, are more likely to mimic each other. That said, I had a set of (girl) cousins who were "mirror" twins and personality-wise were like opposite sides of a coin. One was reserved and thoughtful, while the other was decidedly more outgoing and prone to take risks her twin wouldn't dream of. Naturally they were close and good friends, but were rarely on the same page as far as thoughts and opinions. Also, one was left-handed and the other was right-handed, so their handwriting wasn't the same.