Another piece of anecdata here that middle school was far worse for bullying in my life than high school. However, I may be a bit of a special case because I was fortunate enough to be able to attend a single-sex prep high school (male in my case).
Having only boys in my high school meant there were essentially zero cliques, zero drama, and very little reason for bullying. There was no standing with the opposite gender at risk, and thus very little reason to have the standard sort of extreme pecking orders you tend to find in kids of that age. In all the years I was there, there were literally only two fights (in all four years, not just in my class). One amounted to a guy shoving another guy into a trophy case, so it's stretching to even label that a fight.
Single-sex high schools sounds like an antiquated concept, and I was kind of leery of the idea going into it, but my god, I am a huge advocate now. There was an all-girl's school close by, so things like football games still gave you an opportunity for co-ed interactions, but the days themselves were almost entirely distraction free.
By comparison, my mixed-sex middle school was a nightmare. Interestingly, since they were Catholic schools, many of the same kids from my middle school followed me to the high school, so you can't even simply attribute it to there being a different slate of kids. Some of the kids that were nasty bullies in middle school ended up turning into friends of mine by the end of high school.