I'm female and I get along well with both, though varying by context and from person to person. My circle consists largely of straight men and women, with a smattering of LGBTQ friends.
Friendships: My strongest and longest lasting friendships tend to be with straight women. The implicit acknowledgement of no sexual future can make it easier to discuss relationships, which tends to be a focal point in my friendships with women. I get along very well with men of all orientations, although the When Harry Met Sally cliche that men and women can't be friends because sex always gets in the way has a kernel of truth. There have been several times when men I've been friends with for years suddenly have the revelation that I am, in fact, a girl--"you're attractive, we know each other, you like guys too right?" pops up and then the friendship never completely recovers. Sexual tension can be fun, but it's best left unspoken.
Romantic Relationships: The simple answer is that women make better fuck-buddies and casual relationships partners for me. Those situations tend to be more complicated with men. I've had serious long-ish term relationships with both men and women, and have got along with varied degrees of success that have more to do with individual wants/needs/attitudes than with gender.