Hercules, one of my best friends is the deputy head of a very posh private school where about 30% - 40% of her intake have an eating disorder.
The reason she went into the private sector was because she wanted to teach, not to be a social worker, psychiatrist, security guard, etc.
In the main, there's no doubt that her working conditions are better than what I've heard of many state school teachers, but the problems are different. She has very abusive parents to deal with, but they're abusive in a coherent, structured, legalistic way, where they leave her in no doubt that she's their servant, they're paying her bloody good money to get results, and if they're not forthcoming, that must be her fault.
She also has the psychiatrist job - some of these children feel so terribly starved of love, I know that's an awful cliche and I don't want to start any controversies about ambitious parents etc., but bulimia and anorexia is absolutely rife as it's the only way these girls have of controlling their over-structured lives. There's also a massive drug problem, but again, it's just not "in-yer-face".
She gets straight A's nearly all the time though and the satisfaction of enormously motivated pupils. But I guess what I'm trying to say is that there are still problems, but just different ones (and sometimes, just as heartbreaking ones - a couple of years ago she had an attempted suicide from one of her best pupils), and it's really which sort of problems you feel better at dealing with which would decide what sort of environment would suit you. And I agree with Yorkiegirl, it might just be a change of school you need, rather than of sector.