On twist rate needed, it depends first and foremost on the length of the bullet, secondarily on its the weight, and least on its muzzle velocity. When people ask how heavy a bullet they can stabilize with their barrel's twist, they don't realize the question carries the implicit assumption the bullets they are comparing all have the same proportions, because only then do length and weight correlate.
In reality, with a given twist, you can stabilize a heavier bullet if it is shorter in shape. For example, a typical flat base bullet is shorter for its weight than a typical boattail, so you can fire a typical flat base that's a little heavier than you can a boattail. You could, for example, shoot the 64 grain Berger Match Varmint bullet (flat base) and for which Berger recommends a 12" twist, and actually get a higher ballistic coefficient than you can with the 55 grain boattails available. The problem is, you can't shoot the heavier bullet as fast, which costs you most of the BC advantage.
Second, when it comes to wind, all that matters are the ballistic coefficient and the muzzle velocity. In both cases, bigger is better. If you have a .224" bullet with a ballistic coefficient of 0.4 and a .308 bullet with a ballistic coefficient of 0.4 and you fire them both at the same muzzle velocity, the effect of wind on both will be exactly the same. Differences in weight and wind drag are all taken into account by the ballistic coefficient. Where the bigger round beats the smaller one is in how much energy it delivers to a long range target. For sniping that becomes important.
One other advantage for the .308 is its typical 10" twist is comparable to a 7.2" twist in a .223. It comes ready for long bullets, standard, so length for standard ammo was never a design limitation with it. As a result, 150 grain .308" ball bullets typically have a BC about 0.1 higher than 55 grain .224" ball bullets. At 600 yards, and allowing that the .224" bullet will be starting out faster, figure that where a 10 MPH wind blows the 150 grain .308 ball about 3 ft to the side, it will blow 55 grain .223 ball about 4 ft to the side. That's not exact, but should give you some rough idea of the difference you are dealing with when you are limited by a 12" twist.