I have a Ruger No.1 varmint in .223. It is plenty stout, but the 1-12 twist barrel does poorly with bullets heavier than 55 grains. 5.56 NATO (the REAL stuff with the circle cross headstamp) has always been a 62 grain bullet. This goes back to the late 70's.
" In 1977, NATO members signed an agreement to select a second, smaller caliber cartridge to replace the 7.62×51mm NATO cartridge.[8] Of the cartridges tendered, the 5.56×45mm NATO was successful, but not the 55 gr M193 round used by the U.S. at that time. Instead, the Belgian 62 gr SS109 round was chosen for standardization. The SS109 used a heavier bullet with a seven grain steel core for better penetration against lightly armored targets,specifically to meet a requirement that the bullet be able to penetrate through one side of a steel helmet at 600 meters. It had a slightly lower muzzle velocity but better long-range performance. This requirement made the SS109 (M855) round less capable of fragmentation than the M193 and was considered more humane."
So, if you are shooting an older, slow twist, .223 will be what you want, not the 'green tip' your National Guard buddy cadged from last AT.