I think that's true of many people.

But I suspect that the numbers are pretty evenly split between "would thrive in either role," "would be miserable in either role," "would much prefer being in the paid workforce," and "would much prefer being a stay at home parent."

My wife and I are squarely in the "would much prefer being in the paid workforce," because we like our jobs, and because we want our children in an organized school environment (and paying for after care is fine for them and for us). Most of our social circle are in the same boat. But most of us are mid-career white collar professionals and have better than average flexibility over work hours and location (at perhaps the cost of a blurred boundary between work and home). So our jobs are easier to balance with parenting.

On the flip side, home situation matters a lot, too. How much you enjoy different types of household work (cooking, cleaning, home improvement/maintenance), different functions of a caretaker (feeding kids, scheduling out activities, being that first line as an educator or first aid or driver, etc.), how well your hobbies and interests fit into a lifestyle as a full time caretaker, etc.

One of my friends gave up his main career to take care of his kids, but now that they're in school he went back to personal training at a gym. He lines up clients and is only available for sessions between school dropoff and pickup (10am to 2pm). It's a good intermediate holding pattern for him, and he'll likely go back to his main white collar career once his kids are old enough to be latchkey kids. That being said, I know he wasn't super happy not working outside of the home, and this personal trainer thing has him in a much better spot than when his kids were too young for school.