I have had several 700s built and have owned 4 Coopers. The Coopers will shoot as well or better all day long.
Which Cooper does your friend have?I have owned 5 custom rifles and 2 custom smokeless muzzleloaders. All but two were built by McWhorter and all shot great.....1/2MOA on a bad day....usually better. Actions were Stiller, Borden and Shilen.
All of that said, the most accurate rifle I've ever shot is my friend's Cooper .280ai.
I would buy a Cooper before going the trued Rem700 route.....it should hold its value better and Cooper will take care of you if something goes wrong.
But I have no doubt u can get a fine shooting rifle using a good builder and a REM action.
Good shooting rifles are like good looking women....they're all outstanding....it just depends on your personal preferences.