I had one in public, one in private for several years, and now I have two different privates (MS/HS).
The kids are very good with it. They've been happy with their schools and social circles, so no sibling issues for us. I have one of each gender, but they are both in coed schools.
Logistics are trickier. If you work, it's especially hard and seems like someone is always having a day off. We have never had the same spring break and now they are too old to let one miss several days to work something out. Mornings are fine, each parent takes a kid, and we've been lucky with the schedule this year, I can get between schools with half hour difference in dismissal. The way the schedule was supposed to be, my MS was going to have to take public transportation home, so one Covid benefit was kicking that down the road a year. Many schools have bus service, it just happens that with my location, it makes more sense to take metro bus.
I can really see my younger kid going to the same HS as the older one and that could be the two best years of my life
Truthfully, my kids have always been in the best school for their different needs, and I wouldn't change that unless I really couldn't swing the logistics.