I normally don't have any input for topics like this, but if I were in the posotion of having to choose between a plain wood and synthetic stock, I'd choose the synthetic. I currently have my friends 243 synthetic stocked Handi in my closet, been doing a good bit of cast shooting with it. I notice that the rifel shoots well regardless of what the weather has been, I cannot say that for four other rifles I have, two of which have the laminate stocks. Even though I have sealed the laminates with low gloss spar varnish, they still seam to shift around a bit with hot/cold/dry/wet/ conditions.
It is obvious that whoever had the 243 before my friend had added weight to the stock, and this is a simple thing to do that does have a real influence on the recoil, as does adding a better recoil pad. I also like the non slip surface of the sythetic.
As to the chamberings, it must be kept in mind that the 308 was originally developed for the military, the requirement being that it must drive a 150 grain bullet to 2700 fps, the standard loading for the 30-06 at the time. The intent was to create a box magazine fed rifle, as opposed to the clip system of the Garand, and it was felt that a shorter case would facilitate more reliable feeding. The 308 was meant to be a short case 30-06, and so it is.
As deer rifles go, I can't imagine there would be any difference at all. a 150 grain bullet at 2800 fps is a 150 grain bullet at 2800 fps, as is a 180 at 2600. Both of these have long histories as service and game cartridges and I can't imagine that a failure of either in the game field would be a result of the ballistics either is capable of.