Dpends how many points in your account you have -- But I would say a definite yes!
First, there is a pool in the County Hall -- great for kids. Second there is a McDonalds, also, I think! Need I say more? Third, there are lots of street performers around the County Hall because of the London Eye -- and some typical tourist things that a kid would love, and finally, there is that view, that you would have from your room -- or when you walk out of your room.
As much as I love the Chancery Court -- and I do -- it is in a purely business area, no charm whatsoever. Great for old London hands, but come on, to walk out or stare out of your room and see Big Ben -- not to say, to just walk around that area, and then have a short stroll back to your hotel?
No comparison -- Go for the County Hall.
The Chancery Court will always be there, but your son's youth and inquisitiveness will not be.