The grass can appear greener on the other side. I've been to both public and private schools (got transferred to private when I was almost a teenager) and I'll say this much of my experience:
-the private school was better maintained and had newer equipment
-both taught a whitewashed version of history that was borderline propaganda
-aside from the basics both taught loads of impractical nonsense that you forgot about some time after the test/assignment
-both forced you to scuttle around from one class to another when the bell rang at regular intervals
-you still had to sit down and passively learn crap in both
-the private primary then secondary schools I went to were Christian, so I also had to deal with their religious nonsense
-the kids at the private schools were unsurprisingly from more wealthy backgrounds, but there was still plenty of bullying, exclusive cliques, popularity contests and other nonsense that I tried to stay out of
Granted I only went to what were considered "decent" private schools in the area, and while they certainly had much more resources to play with than the public school I went to before they still had many similarities.
I suppose above the regular or decent private schools you also have the incredibly expensive and exclusive "elite" schools but of course those are only available to a tiny handful of wealthy and well-connected people.
EDIT: screw it I'll add this too. The girls in their uniforms at the private schools looked hot as hell, especially in the winter when they wore stockings. So I suppose apart from better equipment the private schools had that going for them as well ^.^