Surely working is much harder.
Taking into account a scenario with a partner who is happy to work, and you can afford your arrangement......the following is true, I think:
If you stay at home you can spend time volunteering with sports or clubs your kids enjoy; join the PTA, be actively involved in their world to help them. You can volunteer at their school, when they are primary-aged, reading in younger classes, getting to know how the curriculum and school policies work from the inside, so you can support your kids. Then, when they are all a bit older, you 'll be equipped to get yourself a job as a teaching assistant, with those lovely school holidays. You won't have the pressure of HAVING to work - presumably, if you can be a sahm in the first place. And no worries when the kids are ill and annoying your employer by taking time off.
You can work in an enjoyable capacity; volunteer; look after your health by going to the gym when it's quiet; get the best bargains by having time to go around various shops.
The only big downside, I would think, is if you split with your partner, you are not as well-prepared to improve your earnings.