Hmmm...I'm on the adult side so if they are younger than 9 then they go down to the Children's School unless their parents buy them a private lesson which the children's school is not equipped for except on slow days. Still 9 is pretty young, and I have done some privates as young as 3 (I know).
I also coach a youth program where I have the same kids all day on a Saturday for 8 weeks. I think that is my favorite program, those kids all advanced skiers are usually in the 8-10 age group, although I've had both younger and older. They have the stamina to ski the whole mountain practically nonstop (keeps me in shape) and are at that stage where the drills we do really seem to make a difference, you can see the results at the end of the program. Some of those kids go on to work for us as instructors.
During the week we get kids of all levels and ages from elementary through High School who take Skiing as a PE credit (two hours of lessons/lunch/two hours of free ski or vice versa) those too are some of my favorite programs as you are with them for a good chunk of the season, we even give them report cards.
Adult lessons come and go, (with the exception of some privates that return again and again) and I enjoy doing those too, but nothing beats getting to work with the same skiers, some all day long, week after week.
My least favorite? The out of shape teenager from sea level who doesn't want to be there, I'll take an out of shape adult from sea level who does want to be there any day over that!
But really I have no preference. As I moved into supervision for part of my work week I have noticed that generally, the younger staff seems to like working with kids more than the older staff (could be that the younger ones need the money more and take any & all work) but we have some great older instructors who have amazing energy to keep the kids interested, particularly all day long and so I think a lot of that has to do with physical and mental stamina. Our season-long weekend youth programs require that you ski with and supervise them all day long, eat lunch with them and sometimes most exhaustingly deal with their parents.
Teaching approaches are different too, If I were to generalize in the big picture kids: little talking/lots of skiing and fun. Adults: more of a paced approach, some really want/like/need a lot of explanation and the rest breaks. As someone who does this as a full-time job Nov-April, I'm just grateful to have the opportunity to do either!