Technically "We had a burglar in our home last night" is not forward enough to answer the question "did you get robbed?"
The thief may have gotten caught. He may have been a guest at your home and robbed someone later (or taken the night off.) So "A thief BROKE INto our home last night" says more - though we do not know if he/she was successful. "We WERE ROBBED last night" answers more questions. Both sentences are correct.