In a lot of ways I think they do. Mostly because each have strengths that are the others weaknesses. When you feel you have weaknesses and meet someone who has those as strengths in their personality, it is easy to become captivated by them. Sometimes just speaking with the person that has an opposite personality is very interesting. However, it can also be a source of conflict. For example, if you don't argue/fight the same way, if you don't share emotions the same way, if you can't reconcile obvious differences, if life goals aren't the same. Its very difficult to maintain this type of relationship for long term. However when I see my parents who are very much opposites, my mother is very warm very affectionate, very much in touch with her emotions and properly expressing them, very extroverted. My father who is introverted can be cold, who does not ever talk about feelings, who is probably the master at concealment, its very isolating for my mom to feel that he is not emotionally supportive. But I honestly think that's what attracted them. They are both so different, and my dad has become slightly marginally better with emotions and my mom has become possibly even more understanding. They both have the same goals, and both have very very strong personalities and a lot of inner strength. Although like any couple they do fight, but neither has ever run out on the other, they've always had a partnership and although sometimes they really get upset with the other, they always have loved each other. Through all of the challenges, they have always loved each other, married for 27 years now, still going strong. So I mean that's an example of a marriage that has lasted, where the peoples were opposites. Although I have seen marriages where the people involved were very similar personality wise, and that can also work very very well, because they agree on everything, but likewise they have very similar weaknesses. My dad has always said he needs my mom because she is the opposite of him, he needs her because she does what he cant and can teach him what he doesn't know. So if you were both the same it would be very harmonious but you would also have similar weaknesses. But automatically being the same simply means you may have easier time resolving fights etc because you both cope the same way. It also means that there could possibly be fewer depending on the personality.
I would suggest the Myers-briggs personality type testing for peoples. For example to ENTJ's would do splendidly together... until a fight erupts, then you get the worst of both persons because the relationship between two really really strong persons may just be Too Intense as their strengths and weaknesses are extreme. But perhaps two ISFJs would do very well together as their personalities aren't as intense and their strengths and weaknesses aren't that extreme.