How others will see it. It was a successful Neil Simon Broadway play. It was a hit movie. It was a hit television series. Clearly, the premise is engaging. The two main characters are exaggerated, of course, but their motivations are understandable.
Felix is an obsessive-compulsive who wants to keep everything in order. Oscar is a fatalist who wants to enjoy the moment, since tomorrow might not be another day. We would rather be Oscar, who seems (sometimes) capable of having a good time. But we commiserate more with Felix, whose neuroses and angst blockade both happiness and lasting relationships.
How I felt about it. The Odd Couple sure looks like a play. Most scenes take place within Oscar's apartment, and feature pages of dialogue. Men are culturally regarded as standoffish, particularly when they are not trying to impress a woman. In this film, though, all grievances major and minor are to be uttered instead of silently endured, and Felix's poker buddies actually care whether or not he jumps from a tall building. The gamblers I know would place wagers on whether his launching pad is the Chrysler building or the Empire State skyscraper.
It is important to Felix that he be liked. His eagerness to cook for his poker friends is an attempt to show his affection for them. Indeed, there is an effeminate side to Felix that makes the entire play subject to a cynical rewriting: The Odd Gay Couple. Alas, such dangerous comedy was not to be. The Lemon-Matthau chemistry was instead reprised in conventional films such as Grumpy Old Men.
Can Oscar and Felix learn from each other? Can Oscar become financially responsible and a good host? Can Felix learn about carpe diem, and stop whining about his back/bursitis/sinuses? The answer is no, despite Oscar's close comments about cigar butts. They can't even appreciate the other's good points. They will remain oil and water, since man's basic nature cannot be changed. Or it wouldn't be funny.