how is bruno's costume similar to father's uniform? what could this symbolize

I think simply he reflects his father, "You wear the right outfit and you feel like the person you're pretending to be."

Also it is important to note that when Bruno puts on the striped pyjamas, he feels like a Jew. Both worlds are reflected by his costumes.

Actually this quote came from Bruno's grandmother. For his father, the uniform reflected power....... for Bruno, putting on the striped pajamas meant he was pretending to be on the other side; he was pretending to be a Jew.

"I suppose that's what I'm doing, isn't it? Pretending to be a person on the other side of the fence." Page 205