If it's not too late, here's my 2 cents:
Personally, I'm not a pony person. I find their temperament to be difficult to work with. Stubborn/bull-headed. GENERALLY speaking. I see my friend's daughter ride her 12hh (?) pony and fight with it all the time, but she gets on my 14.3hh mare and has no issues at all.
If your kids end up loving the horse/pony they would feel bad if they outgrow it and have to give it up.
If you feel that either animal is a good choice as far as temperament, training, health, etc. etc... since you are shopping for the kids, let the kids tell you. Not in so many words, but let the kids visit, lead, groom, ride both and see what reactions the kids have with each.