Given those two choices I'd go with the Remington 700. My buddy has a Rem 700 SPS Tactical (AAC edition) that shoots pretty well. The .243 is also a proven long range cartridge.
Or, consider some other options:
My Tikka has hands-down been the best off the shelf store bought gun I've ever owned (save for my Accuracy International AX, which I guess could be considered "off the shelf", but is clearly in a whole different category of rifles).
Also, if you really want to shoot small groups:
1) Get good glass… Seriously. Too many people buy a nice rifle and throw a $50 scope on the top, then can't understand why they aren't shooting well. You don't need to spend thousands on your scope (though it can't hurt if you've got it), but you should definitely research the glass you choose at the lower end of the price spectrum.
2) Get good rings/mount for your good glass.
3) Start reloading for yourself, so you can really tune your loads for your gun.
With today's equipment you should be able to achieve 1/2"-1" groups for around $1,000 or so, with some careful purchases, followed by practice and patience.