They have different meanings.
If you are open-minded, you are willing to accept new ideas about something. You might say 'I'm quite open-minded about the relocation project'. This means that you don't have strong views on the topic and that you are happy to listen other people's opinions.
Broad-minded is the opposite of narrow-minded, and it means tolerant. It's usually used with reference to moral and particularly sexual issues. For example, 'Are you really going to see 'Fifty Shades of Grey' with your grandma?' 'Oh, yes, it's not a problem. She's very broad-minded'.