There is a small difference. But even Korean don't know about it. So I think you don't need to worry about that. By the way you can use 멋있다 for women if really she is haha. It's not wrong grammar.

Both expressions mean “to look good” or “to look cool”. I think they are interchangeable in most cases but when it comes to 멋지다, it is often used to describe scenery, or object. 멋있다 is rather used to describe people, or fashion.