In my opinion, the biggest difference is the packaging.

The uncirculated set would have the better chance of higher grade coins since those coins were minted specifically for the sets.
The coins in the circulating set come from the normal production run, so they have better chance of nicks and dings.
In my opinion, if you normally build your sets from circulation and want to fill some holes, the circulating set would be the way to go.
Another way to look at it...
Before this set existed (satin finish fiasco aside), did you feel compelled to buy all of the mint sets
and get the coins from circulation?