I have used both for hunting whitetail deer, (Rem Model 7 in 308 as well as 7mm08/ M1A Socom16/ and 2 other M14 types with 18in bbls)........ and either is more than capable of taking whitetail deer in any state out to your listed range.
I second the notion that you should buy the rifle you really want, and then have the bbl cut back to your desired length....... and for 2 primary reasons.
1. The rifle that feels right in YOUR mitts, and that you shoot well is the more important aspect as compared to either of the 2 cartridges your interested in.
2. If desired, you can have the bbl cut back to the length you want, and also have the muzzle threaded, as it might be something of interest since your out of GA.
I'm not sure if SB93 was passed or not via GA, but the bill would make it legal to hunt with suppressors there if it did in fact pass into law.
Also...... a well built muzzle brake can lend itself well concerning muzzle rise, and to some extent...felt recoil. It will also protect the rifle's crown while your hunting in the thick stuff.
3. Optics: A 1-4x20mm scope provides for plenty of magnification out to 250yards, works well for hunting at closer ranges such as inside of 25/50 yards, and is more lightweight/compact than most 2-7x33's or 3-9x40's.
4. 22LR rifle: Been mentioned here already, but would second this idea as well, and worth looking into ITO hone the fundamentals while keeping ammunition costs down. ( I use a 10-22 fitted with Nodak iron sights for this purpose, and it fits well with my favorite M14S 18in bbl rifle I use for hunting.)
With that said, I shoot quite a bit of the cheaper 7.62x51mm every week, as well as hunting hogs yr around with the same rifle.
FWIW...... I have just recently acquired another rifle chambered in 308. It's not a bolt action, but it is very compact....sporting a 16in threaded bbl with an OAL of 34.75 inches. Weight = 8.5lbs. My 18inbbl M14S is about the same weight, and OAL is right at 38inches as a reference.
A Ruger American compact bolt action rifle ( .243, 7mm08, 308) runs at 6lbs with an OAL of 36.75 inches, along with it's 18in bbl
Ruger's M77 compact sports a 16.5in tube, and weighs out at 5.5lbs.
Do you have a overall weight restriction, or is the focus on OAL ?