or 'We look very alike' or 'We're identical' (if you are identical twins)

I think both of them are correct

Can't read the Spanish(?) but I can tell you the difference between your two sentences. "We look alike" is what we would most commonly say and implies that we look very similar, although there are differences. "We look like the same person" is rarely used and would imply that we don't just look similar we look EXACTLY the same.