Both suffer balisticly from short barrels compared to what published ballistics on those caliber's are. 223 falls way off in the energy delivered to target area and has much less mass for follow through. So.. If hunting is your goal (deer, hogs) you can deliver more potential energy to the target by throwing a heavier projectile. Most likely..?
Don't get me wrong. Both caliber's out of 12" barrels will kill Deer and Hogs. Just have to pick and choose your distances and shot placement with a bit more caution.
IMO...if .223/5.56 I would go 1/7 barrel and 62gr-75gr projectiles. 308 I would back off on the weight to 120-130 in an effort to pump up the velocity a little. You may well find expansion issues when you get the point of impact velocities below 2000 f/s so running ballistics calculator for various loads is helpful.
Personally I think 308 has more options available but then again if hunting with a short barrel...6.8spc, 6.5 Grendal or even 300blk may deliver just as much energy at POI in a smaller platform than a 308 rig.
Start crunching numbers and it will become clear which fits yor needs and desires best.