You are pretty much describing me and my partner when it comes to the introvert/extrovert thing. Mostly I think it works for us although I am still not sure he 100% gets what it means to be an introvert.
We don't live together, but I spend at least half my time at his house. He doesn't mind interacting with me ALL the time and sometimes I have to say to him that I really want to be alone, or have suggested he go talk to some other friends LOL. Luckily he doesn't take offense. He worries sometimes about leaving me alone if he wants to go out and I am usually like--no REALLY, please go out. I will be fine! (In my mind: I can't WAIT to be alone finally!) We find humor in it.
My introversion helps ground him I think and his energy and extroversion does help me get outside of myself, and outside of the house so I am not a shut in.
He is also a very thinking/logical person and I am much more feeling/intuitive person. This CAN create many problems in communication, but it can also be good because we are each good at different things and help each other out.
We both do creative work (I'm an artist, he's a furniture conservator), but we do different kinds of work. He has to be very precise and also knows how to build things and I am really great at color and take a lot of risks. We have found that we both have assets the other doesn't have we have both helped each other out in projects.
He's a meat eater, I'm a vegetarian. That we just have to accept about each other, though when he picks up pig heads from the local butcher it's rather disturbing to me. But he cooks a lot of vegetarian stuff for me, which is nice.
What else? We are both fairly neat but not neat freaks so we don't have any Odd Couple issues there. He's 17 years older than me so there can be generational issues at times. With pop culture we are in two totally different places. Half the time he doesn't get my references and half the time I don't get his. He will ask me about a TV show for instance, that I have never even heard of. And I will ask when it was on. He will say "Oh in the early 70's." And I will have to say, my love I wasn't even born then LOL.
He also LOVES telling stories. Over and over and over. I prefer to communicate concisely and when necessary. I have a rule now where he can tell me the same story three times and then I reserve the right not to listen. Sometimes I will sit there for a while before I can't hold in the snickering and he will say "Oh, have you heard this one before?" Oy vey.
But on of the things I love most about him is that he lets me laugh at him.
He's an optimist, I'm a realist.
Really, our relationship is very complicated and the differences can be difficult. But I think on the whole we benefit from them when we remember to accept each other and also have a sense of humor! To me, it's beneficial to be able to draw on each other's strengths--we have gotten each other through difficult times that way and have also helped each professionally with interesting results.
I doubt I would want to be with someone too much like me! We'd just exist in opposite ends of the house reading books and never speaking or going out LOL.