In my opinion, the Rem. 700 is typically quite a bit more accurate and has a better trigger "out of the box". I recently sold a Ruger 77 International and replaced it with a Rem. 700 Classic, so right at this moment I may be a bit biased--the Ruger wouldn't group for shit (pretty sure a bedding issue with the Mannlicher style stock), with ANY factory loads I tried which was many. The new Rem. loved my handloads (already loaded for another rifle) from the first try. Didn't even try factory loads.
My other 700, a BDL, Has the best trigger I have ever felt on a new out of the box rifle, and is a grouper also.
But, my wife loves her stainless 77 M.II, even with its six or so pound trigger (and she can hit with it--she told me "don't mess with it or get rid of it")
ETA: I believe the .243 is a very under-rated rd. and is a true handloaders cartridge
MY 2 CENTS