I am a stay at home mom by choice, having turned down employment offers. I also work from home, but choose my client load.
At one time in my life, I attended college full time and was the Program Director at a Chamber of Commerce -- I will tell you now, being a stay at home mom is much busier and more challenging -- and more rewarding.
I find the mental stimulation from projects is beneficial to my well being, and thereby, benefits my husband and family. I don't think compartmentalizing everything is healthy or accurate. My husband enjoys seeing me work and the satisfaction I get from a job well done. He also loves seeing me with our children. We have 5. We only have one vehicle currently bc we do not have the cash to buy another, and do not want payments. We agreed before we ever married that (a) we wanted at least 4 children, (b) we would do all it takes to keep them home and not in daycare. It's not always easy, but I don't regret it. But - to answer your question -- I suppose I do partly both -- with the majority being SAHM.