I am a pony person!, actually both are ponies, if the small horse is 14 hands its a large pony. Usually large ponies are more popular and sell faster than the smaller ones. (I know I have been looking for a nice large pony for a while) With kids that young I would opt for the smaller one. It helps them build confidence. Yes they will out grow it eventually and more quickly than the larger one. But honestly they may lose interest sooner than you think anyway.
Are you small enough to ride the smaller one? Most ponies can carry 150 lbs w/o issue. I would suggest you or some more advanced rider working the pony on a regular basis, unless its an older dead quiet pony.
I went from small pony to medium pony before going to a small horse and I enjoyed my ponies the most of any mount I have ever had.
Also the smaller pony will be easier for your little ones to groom, bathe, etc.
Just my 2 cents. Got any more details/pics of the two in question?