Most that know me know that I am a very big 308 fan. 708's are great too, but in these medium calibers its best to stick to a much more narrow spectrum of bullets for optimum performance. The 162 AMAX is an awesome bullet, by far about the best choice for the 708 and deer but you had better hope that bullet shoots well in your 708. For me, 1 choice is not good enough.
If you should go with the 308, stay away from the 168 for beyond 300 yard hunting. The 155, 178 AMAX and the 175 SMK as well as the 190 SMK are awesome 1000 yard performers. I have a 190 SMK load that delivers 2657 FPS, has over 1000 pounds of energy at 700 yards and only drops 112" from a 300 yard zero. I also get 35" of drift for a 10 MPH wind also. This load is VERY hard to beat, esspecially when it averages 0.5 MOA at 1K.
Good luck!