I've experienced both and it is nice being with someone who you can share that part of yourself with. *Chuckles* My current mate and I often refer to each other as Miss Kitty and Mr Skunkie when we talk.
However, the main thing with any relationships is to have and foster shared interests and experiences. For most of us, furry is but one aspect of our lives and there area many other areas that a relationship can be built upon.
I've learned first hand the importance of fostering and maintaining shared interests. My soon to be ex-wife and I stopped working on finding and keeping things in common over four years ago and our relationship deteriated quickly over those years until we were nothing more than roommates living in the same house. There were other problems that led to the situation, but the lack of things in common when we actually looked at the relationship and saw how broken it was helped in the decision to separate. It just didn't look like there was a strong foundation to rebuild upon.
I of course agree with everyone who says you can't separate furry and human. We are all human, it's just that we have a love / indentification with anthropomorphic characters as well.