I have to assume that Atwood's Moral Disorder and Other Stories was inspired by Munro's The Lives of Girls and Women. Both are collections of short stories about a single female character (Nell in the case of Moral Disorder) and their immediate families. However, the connection might actually be closer to Who Do You Think You Are? (also all about one girl -- and her fraught relationship with her step-mother), in the sense that the scrambled chronology allows the authors to move back and forth in time, and in particular showing how the main character must deal with aging parent(s). One thing that is odd is about half the stories in Moral Disorder are written in first-person perspective and half in third-person.
I would say that on the whole there is more humour in Moral Disorder, or at least a lighter touch. That said, there are definitely tense and difficult moments between women, such as when Nell mouths off to her mother (about not wanting to take care of her baby sister) and gets slapped hard or when Oona (Nell's partner's ex-wife) starts making trouble between them. One thing that I do like about Atwood is that she doesn't sugar-coat the fact that women can be terrible to each other (not that I think the moments I have referenced really rise to that level). This is a bit of a recurring theme of Lady Oracle and Cat's Eye, though Cat's Eye the focus is on younger children behaving badly. Munro occasionally delves into this (as in Who Do You Think You Are?) but my overall (perhaps unfair) impression of Munro's work is that she sees male-female relationships as inherently more difficult than female-female ones, and I don't think Atwood would agree with that.
The stories are set in Boomer territory, so Nell comes of age in the 1960s, which means that she benefited from women entering the workforce in a wider variety of roles (Nell is a bit of an itinerant academic who does some work as an editor (and ghost writer?) and instructor) but also from living at a time when the workforce did seem wide open and the cost of living was generally low. Cultural norms were changing as well, and many marriages were foundering on the rocks of free love. Indeed, Oona and Tig had a bit of an open marriage (despite having two children) but Oona decided she wanted more freedom, and more or less auditioned Nell to take her place (in "Monopoly"). Not that everyone was completely on board with these changes. Nell's parents disapprove of her living out of wedlock with Tig. (Indeed, I can't tell if they ever did officially get married, though it seems likely.)
One interesting aspect of Moral Disorder is that Atwood shows how people can change their minds (which happens a great deal in real life but not always in fiction), and Oona comes to feel she got the raw end of the bargain. While Oona and Nell have long ago stopped talking, Oona uses the children to guilt Nell into buying a house and letting Oona move in as a tenant ("The Entities"). The story actually goes in quite a different direction than I was expecting, given that Nell is too much of a pushover in general. This tendency to just be too nice is also on display in "The White Horse," where Nell and Tig are living out in the country and doing a pretty poor job of living off the country and taking in animals that are more trouble than they are worth. I have to admit that I have so little connection to the country that I was somewhat bored by "The White Horse" and "Moral Disorder." I was very glad when they sold up and moved back to Toronto.
The last two stories basically focus on Nell's aging parents, though in the case of "The Boys at the Lab" it is more of a memory piece where Nell remembers her father and his work as a biologist, living in the woods. This is of a piece with Cat's Eye, so I suspect Atwood is writing another tribute to her father, though from a different angle. The focus is on memory and trying to recover what was known as opposed to what was unknowable. Her mother is generally not able to answer the questions Nell asks, and her father had passed on several years back. I suppose more than anything it is a reminder that one should ask these questions while members of the older generation still have all their marbles.
The single biggest surprise to me is how small a role Nell's daughter plays in these stories. She is an adult "busy with her own life, elsewhere" in the first story in the collection "The Bad News." Then the next 4 stories are mostly about Nell's childhood and very early adulthood, prior to meeting Tig (with some flash-forwards to the present). The next three are about meeting Tig and moving to the farm. We find out that Nell wants a baby in "Moral Disorder", and then she is going to have a baby in "The White Horse." However, unless I have completely blanked on it, there are no scenes of her with her daughter as a baby or a small child. The next story is all about Oona coming back into Nell and Tig's life, and then the final two stories jump ahead in time to when Nell is dealing with her parents. So that is a strange absence at the heart of this book. Aside from a bit too much time spent in the countryside for my taste, this was an interesting book about an unconventional family, living through a period of significant cultural shifts.