I have a Cooper 52 in 338-06 and really like it. It's more accurate than I am with it and Cooper has very good customer service, in my experience. If I were to change it, I would prefer to have a 3 position safety that allows the rifle to be unloaded with the safety on and also provides a bolt lock, so you don't accidentally bump the bolt open when packing thru the alders with it.
The Christensen Arms rifle sure look good and well made. I've never shot one but they are reported to be very accurate. I've never been attracted to the carbon fiber barrel versions personally, but that's just me.
With only having experience with the Cooper's, My recommendation would go to them, but like Jim said, You won't go wrong with either one.