Captain Stubing, here's the finer details of both the Remington 7xx and Winchester 70 (and its 670 & 770 versions) compared from what I've observed with both of mine as well as many others on the rifle ranges.....
Firing pins....The Winchester one can be replaced without tools. With a hammer, drift pin, a penny and pair of pliers all on a table or something, the one in a Remington can be replaced.
Extractors....Remington ones broke a lot and needed a few tools to both remove and replace. The early Winchester ones could be replaced without tools but those made from 1964 with the push feed bolts need a paper clip or a pencil to replace it as well as its spring and plunger; very reliable in operation and rarely, if ever, broke.
Box magazines....Winchester ones fed the most reliable but needed their follower top ribs for .308 and .30-06 rounds filed to a 45 degree angle to prevent round stacking when charged with 5 rounds in a hurry. Remington ones oft times hung up rounds at the top front of the magazine box.
Safeties....Remington's early safety design was poor and didn't lock the firing pin directly so it caused too many accidental firings. And with the safety on, the bolt couldn't operate to unload the magazine. Its designer came up with a fix that cost an extra 6 cents per trigger to make but Remington chose not to do it. Winchester's was the most reliable as it locked the firing pin back, plus, the safety can be engaged then the bolt operated to unload the magazine.
Recoil lug....Winchester's would take the force of a .458 Win. Mag. in hot temperatures all year long wearing out half a dozen barrels and never fail 'cause it's intregal with the receiver. Remington's is a separate piece that has bent forward from 400 rounds or so of .300 magnum use.
Rear tang....Remington tangs are not all that stuff; they've bent with too much torque on the rear stock screw. Winchester's are rather strong and hold up well with even tight torqued rear screws.
Bolt operation....Winchester's bolt is longer and better designed for most humans to reliably operate it in rapid fire situations without miissing a stroke. Remington bolts are too short and sometimes their knob's missed in a quick grab for a quick second shot so they need to be lengthened half an inch. Winchester's claw extractor and external ejector in their classic actions allows fired cases to be pulled all the way out for easy removal when single loading while the Remington clip extractor and spring loaded plunger ejector flip the case out as soon as its mouth clears the receiver ring just like the post '64 push feed Winchesters.
PS: Yes, I like Winnies. But a good friend who fired the last shot to win the 1972 Olympic Games' last 300 meter free rifle match in Munich, Germany (he shot a 10 after taking apart his Rem. 40X and fixing something then getting it back together just a few seconds before time ran out) loves his Remmy.