Ah this falls into the classic 'clone personality' trap:
People often, wrongly, make the assumption that a clone would have the exact same personality as its base, but this is overly deterministic. Certainly there are some, very limited, aspects of our behaviour which are determined by biology, but almost all of our personality comes from our experiences. Whilst the clone shares your personality exactly at the moment of its creation (since it's brain has the exact same composition, including memory, as yours upon 'birth'), it starts to develop a separate, but related, personality from yours as soon as that instance has passed. This personality grows exponentially as time progresses until it starts to look very dissimilar from the personality it started out as: just think how much you've changed in the past decade, or perhaps even the past year.
For a more tangible example, imagine that your new clone and you read two different articles in New Scientist. Your clone reads about the attention-switching capacity of dogs and you read about super-symmetry (I picked those because I read both and enjoyed both, so presumably so too would my fresh clone). Your clone now possesses knowledge that you do not and vice versa, you now have something to talk about because you are no longer duplicate personalities.
The 'female me' would face the same problem: she wouldn't remain 'me' for very long, she'd fast become a separate approximation of me based upon what she experiences after becoming a separate being. So, yes, I'd date her because she'd be enough like me that I'd get on with her logical, skeptical nature, but not so similar to me that there'd be nothing fresh to discuss.
The glorious and ever-sexy Daniel O'Brien sums it up like the voracious He-Man he is over at cracked [http://www.cracked.com/blog/human-clones-do-you-fk-or-fight].