It depends. If it's someone of my own sex, then I don't like that, but if it's someone of the opposite sex than myself, I don't care as much.
I think it's because I feel like I can't/don't want to be a man, so if someone wants to be with a man, I'd rather them just go be with a man once or twice. However, if someone is going to choose another woman over me, it makes me feel inadequate. This goes for if I date a woman or a man, as someone who dates both!