I have been instructed that faster means lighter bullets, and slower means heavier bullets for great accuracy.
Its the opposite, BUT, it has more to do with length then weight.
For example, lets say you have a 150 grn round nose, flat base bullet, and compare it to the same caliber, 150 grn spear point, boat tail bullet. The later is going to be longer and would require a faster twist to stabilize it or keep it stable.
Also, a faster twist will stabilize a shorter/lighter bullet better then a slower twist will stabilize a longer heavier bullet.
Taking your 30 cal bullets, a 1:10 will stabilize a 130 grn shorter bullet better then a 1:12/14 will stabilize a 180-190 bullet.
The 223s is a better example. The 1:7 the military uses will stabilize the 50-90 weight bullets, but the 1:12 doesn't preform well in anything over 55 grn.
Manufactures use the twist that will stabilize the widest range of bullets the customer will use. That's why they use the 1:10 in 30 cal. If you were going to make a Palma rifle using the 155s then people use the 1:12 or 1:14. But most people don't shoot Palma, they hunt and want 150-180 308s, hence the 1:10.
Back to the 223s, most manufactures use 1:9 instead of the 1:7. The reason being, the longer, 80-90 223 bullets require the bullet to be loaded longer, meaning they wont fit in the magazines of the ARs and other 223 Gas guns.
Those who use the 80 & 90s use then in competition, 600-1000 yards. They don't care that they don't fit the magazines because they have to single load them in matches anyway.
Another reason for the manufactures not using the 1:7 for everything is civilian varmint shooter may want the super light 40-50 varmint bullets that have thinner jackets. They want the bullet to come apart so there is lest fur damage (the don't exit) and the break up when the hit the ground, meaning less chance of ricochets. A super light jacked 40 grn bullet (made for the Hornet) could fly a part by over spinning, in the barrel or air.
The military doesn't use those thin jacketed bullets. Some military bullets are lighter then others of the same length, such as tracers vs lead core bullet.
A good rule of thumb, if everything else is constant, go to the faster twist.