There are pros and cons to either parent SAH. I don’t think the dad factor means much. It’s more important to figure out finances and what, if any, sacrifices will be made (and if you’re happy as a couple with that lifestyle), how the other person feels being the sole earner, how stable their job/area is at the moment.
Then, you have to really question how happy and fulfilled you will feel staying at home. It’s a trickier question for dads, I think, because most women get prolonged mat leave where they have to stay at home and experience that version of living - the relentlessness, the challenges, the budgeting/lack of income etc. I think it’s easy for some to have an idealised version of SAH parenting when it can be really hard.
I think it’s also worth discussing what time period you imagine staying home for: Is it open ended, is it until all kids are at school? What happens if you have another kid? How would being home affect your wife’s mat leave? Could she be home as long as she wants to be with the baby?
I’d also discuss how you’ll divide labour when one of you isn’t working. How will cooking/cleaning/shopping/laundry etc be divided. How will parenting be split when you’re both home (early starts/night wakes). Mapping this out as much as possible when making the decision will make it easier to understand what you’re actually going to be doing every day/week.
There are probably many more questions/things you would need to discuss as a couple. Of course, having a happy engaged parent at home when your kids are young is a huge pro for them if you can afford it and if the parent staying home is happy to do it. It can also help the working parent focus on their career more if they are driven in that area.