I'm with SmilingBoy: go for the short connection - especially since the ORD flight leaves just a little later (12:15) if worst comes to worst and you miss the IAD flight.
I did it yesterday: arriving from FRA at 11:15, and connecting to the ORD flight - absolutely no lines at passport control and fairly quick extra security at the UA gates. And since the extra security seemed to be just for the UA flights, I doubt that they wouldn't make sure that everybody gets on the plane...