The original twist of the .223 Remington was actually 1 in 14" and the first M-16s (actually AR-15s) were made with that barrel twist until it was discovered that the 55 grain M-193 bullet (a boattail with a fairly long ogive for the time) was not adequately stabilized at very cold temperatures. For this reason, the twist rate on the M-16 was increased to 1 in 12".
This worked well until the 5.56 was adopted by NATO with a Belgian designed 62 grain bullet with a partial steel core known as the SS109 (M855 in US parlance). Due to its length, this bullet was found to perform best with a 1 in 9" twist, coincidentally the tracer round adopted at the same time needed a 1 in 7" twist for optimum performance, so that's what was adopted for the M16A2.
When people started having true match grade barrels made for this quick twist (and Sierra started making heavy, accurate, high BC bullets), it quickly became apparent that a properly put together "Mickey Mattel" was an excellent long range match rig and it pretty well ran the M14 and 7.62x51 off of the 1000 yard firing line (at least until late 2001 when American troops started to encounter targets that shot back and were so lacking in sportsmanship that they hid behind things when shot at).
It's getting late, so I'll cut to the chase. If your intent is to use the weapon as a traditional .223 varmint rifle, IE: with highly frangible bullets of 55 grains or less that are effective on game up to coyote size out to maybe 350 yards if the wind isn't too bad, get the 1/12" barrel.
If you'd like to use the weapon for hogs and small to middlin' deer as well as some long range target work, get the faster twist rate barrel. The quick twist barrel can shoot most of the same bullets as its slower twist brethren with the possible exception of light, thin jacketed "Super Explosive" types (which can be very useful if you want to avoid ricochets). The only other downside is a possible decrease in accuracy with the lighter bullets as compared to a slower twist barrel. My experience has been that this difference is less noticeable with higher quality, more accurate bullets.
The 12" twist barrel isn't likely to be as versatile as the 8" twist. They are generally hopeless with any high BC bullet of more than 60 to 65 grains, but most of them will do pretty well with the Speer 70 grain semi spitzer, a bullet that has given me very good results on hogs larger than what should really be shot with a .22 caliber rifle.
If you'll be using the rifle mainly on varmints or very close range medium game, the 1/12" has some definite advantages. I love the Speer SX varmint bullets for truly spectacular "meat shower" performance on P'dogs and other small varmints combined with virtually zero ricochet.
The 1/8" twist will give you a bit more versatility and extend your range considerably over the slower twist, especially in windy conditions, it'll make a far superior long range target rifle.
Sorry if I've waffled a bit in this post, but I like 'em both.
You pays yer money and takes yer choice...