Neither. Now, I'm not trying to be a negative nancy or bash either gun. But I've owned both, and didn't own either one for very long. I'll list my reasons; what it really comes down to is that a true custom can be had for a very similar price. A lot of it is because I'm very picky about guns, and there are certain things that I think have only one proper solution.
Cooper Negatives:
1. Junk magazine. Seats poorly, mine fed very poorly. Prone to seat crooked.
2. HS stock is heavy, ergonomics are nothing to write home about
3. Barrel isn't threaded. Not everyone cares, but it makes my toenails curl, especially on a pricy gun.
I do love the Cooper action, through the bolt stop broke on mine before it hit 100 rds. Trigger was good as well (Timney on the one I had).
Christensen Negatives
1. Poor accuracy (for the price). Mine met the 1 MOA guarantee, but a $2k+ rifle should do better.
2. Garbage magazine (the CF one). Hinged floorplates make me cringe too. AICS is the only way to go, and they don't do that on their hunting rifles. However, Wyatt's will bolt right into place on a Christensen.
3. Sloppy tolerancing. Way too much play in between the bolt and raceway for my taste.
4. Flimsy stock. The lightweight fiberglass stocks aren't loads stiffer than a tupperware factory stock. Mine had all kinds of loose fibers inside, and wasn't bedded.
Timney trigger was nice, and the ergonomics of the stock were excellent. Loved the titanium muzzle brake, and the new ones look to be even better.
The point I want to make is that for money, a much better gun can be had. All the little details that drove me to sell both guns (including less than stellar accuracy from the Christensen) are resolved in a custom build from someone like Bullseye Precision or NW Action Works, who will build a gun in the same price range that will run circles around either rifle. The only advantage I see to either the Cooper or Christensen is that they can be had immediately. However, a year later, I still don't have the gun I want because I wasted a year and several thousand dollars messing around with half baked "semi-custom" rifles.
If it does come down to one of the two, I'd do the Cooper. I think their manufacturing is far superior, and their CS as well. The 1/2 MOA guarantee vs the 1 MOA guarantee says it all about their manufacturing, and how they feel about their product.