Chief Joseph gets the nod to my thinking, but both are awesome rides.
Leaving Yellowstone in July 2010 we spent the night in Silver Gate, MT, then rode Beartooth over to Red Cloud the next morning, ate lunch, and then came back over Beartooth and hung a left onto Chief Joseph down to Cody.
They were working on the roads crossing Beartooth so we got hung up going both ways. Sitting around for 30 minutes in 34 degree temps sucked.
However, after we got on Chief Joseph it was just unending sweepers and almost no traffic.
Granted, our direction of travel was opposite of yours, but I'm glad we did both roads. So yes, the extra 90 miles is worth it.