Both are kid friendly. However if you are thinking ski school or something like that You just can't top Deer Valley. It could be that deer Valley is expensive or becuse it has a rep for being a wimp mountain There seems to be a less aggressive attitude amoung younger skiers there. Theres some excellent teachers that love working with kids. pluse a daycare for those not ready or not into being out in the snow. Also ask for directions to see The Bear house and the racoon house at deer Valley Kids and adults get a big kick out of the creative hand wood carvings of bears Moose Racoons and even a skier up a tree excaping a hungry bear..
One of the things I don't like about the canyons is that many of the Trails they cut for lower intermediate skiers are narrow like the trails they have back east. this can make for some tight spots and hard to get around other skiers. Other then the narrow trials it is an excellent mountain with some vary long and scenic trails.
Park city has a good rep for thier ski school seems that every year they get someone in the 100 instructors in the US. By the way other instructors do the voting on this so you know they have to be good. The Green runs can get packed and there are some agreeive skiers and riders there. They have a beginners terrain park and many of the Green and Blue and black diamond runs are served by the same lift. members of your group can ski what they want and meet up at the bottem of the lift. Out of the tree I would say Deer valley would be your best bet Fllowed by Park City. Someone who skis the Canyons more then i do might have better info for there. Hope this helps