Arco route is less miles but can have much worse weather/roads.
I've driven both ways and I think it is about a toss up in driving time from Pocatello.
I think it would be about 1 hour less driving time through Arco from Idaho Falls to Hailey on good roads.
Google maps says...
Through Arco. 144 mi – about 2 hours 45 mins
Through Burley/Twin Falls. 227 mi – about 3 hours 50 mins
Also on the Arco Route be aware of the "Gannett cut off" A few miles past the town of Picabo, take a right on a road that is labeled Gannett. Ends in Bellevue and saves 5 miles, though slower speed limits so pick your poison.
from:idaho falls to:gannett, idaho to:hailey idaho - Google Maps