Don't the kids wear the same clothes as well?
similar but not the same. His daughter's dress and his son's shoes are different. His son also has a lot more hair than in Cobb's memories.
A number of people have complained the dreams weren't weird enough but I'm sure Nolan made them more real so we would pick up on these little details. If it was all flying dragons and bendy cities the dividing line between dream and reality would have been so clear no one would have even considered the little things like what the kids and Michael Caine were wearing. It puts the audience in Cobb's position on wondering whether everything is real or not.