I personally have not tried that comparison, but I can assure you that I shoot my 6.5 Creedmoor far better than I ever shot my 300 Win Mag, or 30.06.
I agree with what you are saying but I wouldn't say I shot my bigger guns worse as I was able to keep them sub MOA. What I will say it that it is so much easier to obtain that same level of accuracy with my "little" guns that I shoot them more frequently and only bring out the "magnum cartridges" for specific circumstances like extreme cold late winter elk hunts. Even then, I'll take my 6.5 PRC over my 338WM or 338 AX.
We (my wife, daughter, son, and I) have killed over a dozen deer and antelope with the 223, 22 ARC, and 22CM using the 73 ELDM, 75 ELDM, 77 TMK, and 80 ELDM bullets in factory ammo. Carried my pink 223 and my 22CM all last season and never felt "under gunned". I didn't shoot an elk only because I never had a legal animal in front of me.
I came to Rokslide with an open mind. I wasn't here a week and had already bought a Tikka package with a magnum bolt face action and 3 barrels (6.5 PRC, 300WM, and 300WSM) from a guy who jumped into an airplane and flew it up to the airport near me to hand deliver it to me. Thanks again Jordan!
I read the 223 thread and figured I'd try it out. Ordered the cheapest 8 twist bolt action 223 I could find on Gunbroker (used with a scope for $400) and 200 rounds of Black Hills 5.56 77tmk. Took it out and shot a buck antelope with it at 400 yards 2 days later after work. Killed just as easily as my 243, 6mm Creedmoor, 260, 6.5CM, 264WM, 270win, 270WSM, 280AI, 7mm-08, and 300WM did. Got my kids shooting it and they killed whitetail and mule deer with it just as easily they did with their 6.5CM and 7mm-08 only with less mental stress. I am of the mindset that the 223 isn't the the end all be all for hunting but it and other small calibers have worked very well for me and my family.
Jay