Part of the comedy was gender role reversal. Felix acts, in many ways, as the woman in the relationship, doing the cooking, cleaning and nagging. This is partly why he was thrown out by his wife. So in the course of the play, Felix becomes less like a woman, and Oscar becomes more like a stereotypical woman (dressing better, eating more healthy, being cleaner, etc.)
The clash if personalities was also at least partly based on gender role reversal. Most of their arguments revolve around Felix’s “woman-like” activities. Much of humor is based on surprise, and it is a constant surprise to the audience to find a man doing things like cooking and cleaning and nagging (while still remaining resolutely straight in the rest of his activities: poker, women, etc.). All Oscar has to do is react like a normal male slob, and instant humor. (Note: based on 60’s and 70’s American cultural stereotypes.) Add in Felix’s other quirks, like his sinuses and his bad back, and you have enough to fill out the original play and movie.
Therefore, I don’t think this would work as well with women, because it is still not as surprising to see a woman acting like a typical slob male as it is to see a man acting like a female stereotype. So you could certainly write a play based on a clash of personalities between two women (I’m sure it has been done many times) but it wouldn’t be The Odd Couple just cast with women.