Longer response, curriculums are relatively similar, at least in the early years. I think public, at least Montgomery County public, pushes too fast on things like reading. Great if your kid is advanced. Not so great if your kid is typically-developing. But my kindergartener in private school learned very similar things to a public school kid in major subjects.
The difference for us was very small class. 16 kids and 2 full time teachers. No homework, which I'm adamantly opposed to in younger grades. More time for enrichment with things like art, music, language, physical Ed, 2 recesses a day. A disciplinary system I feel comfortable with. A focus on character.
The thing I really like about my child's school is its i quirky-based. So while my son, like kids in public school, learned to tell time and chart weather, he learned to ask why we need to tell time, what are different ways to tell time, how does telling time help us?
And class size matters for the younger grades. But don't pay for private school just to get small class size. While statistically significant regarding outcomes, it doesn't mean your particular child needs them. And they have to be really small to significantly help. 17 and under I think. So don't pay solely to reduce class size from 31 to 22.
I think there is more flexibility in private school these days. My son got to dissect a baby squid in kindergarten, because a marine biologist dad brought them in. We have vast resources of parents in this area with amazing jobs like this, but I'm not sure a public kindergarten class would be willing or able to accommodate that experience in class.
And bottom line, schools are only as good as the teachers. If you have crappy teachers at a private school, you will spend $20,000 a year +/- for a mediocre education. So look to the teachers, their experience, and the school culture with respect to teacher training and support. Those are critical.
There is no perfect school for your child but you can find a great one around here easily.