When they have their first big fight as a couple, Chandler assumes the relationship is over, because he's never had a relationship last past that point.
This may explain his frequent breaking up with Janice -- when it gets uncomfortable, he runs instead of working through anything. Then there's the blissful make-up period, followed by running again if things get too deep (see the page on Chandler and Janice for more about their dynamic).
In my opinion, these issues stem from being the child of parents who divorced when he was very young -- he had no experience with how functional relationships work.
Monica's parents are still married and still happy, so she has seen examples of what to do and not do to make things last. She actually says as much in her toast to them on their anniversary.
Chandler is willing to face challenges he used to run from, because Monica supports him through it. She doesn't just expect him to know what to do. Because she is his friend as much as she is his love. And he knows their relationship is worth whatever it takes.
She loves having control over things like the cleanliness of her apartment, timetables/schedules, and things of that nature. I honestly think this so-called "obsessiveness" and attention to detail help her feel more secure, somehow. I also think she developed the capacity to be so tidy in order to impress her very hard to impress mother. Her mother has an attention to detail that rears its head often in the form of nitpicking what Monica does (hair styles, fashion choices...). This, in my opinion, is why Monica obsesses so about details: she has had to her whole life.
At one point, Chandler discovers a closet in their apartment (which Monica always keeps locked) is filled with a secret stash of Hoarders-level clutter. Monica is mortified he has found this out and fears he will react poorly. Instead, he is amused. He tells Monica he doesn't love her because she's super organized, he loves her in spite of that. It's a great moment that shows just how loved and accepted Monica is by this man. I think that realization that Chandler loves her unconditionally helps her to let go of a lot of her feelings that love from her mother was conditional. Judy is not outwardly a "bad person," but she transferred many of her own insecurities to Monica.
Monica and Chandler are both far better off psychologically when they are together. They play to each other's strengths, compensate for each other's challenges and keep friendship the core of their relationship. They don't just love each other, they like each other. That makes all the difference in the world.