I vote for 308
Not sure why people think 308 can't handle heavy bullets. According to Bryan Litz 220 grain is ideal weight for 308 win. 'Experts' shooting heavies in 308 in competitions prove that to be true. I shoot 208 amax out of my 308, 1/2 moa easy. According to Shooter (ballistic calculator), 308 has 1000 ft lb of energy(lot of hunters will argue but most agree that to be enough with right bullets) upto 700 meters(in my current conditions), that's using my load with 178 grain target bullets, so your results may vary but still 500yards is not a problem for 308. But amax is considered to be decent for hunting, with 208 Amax, 1000 ft lb energy is available upto (over) 900 meters. So if you can shoot it accurately enough, deer sized animal is within kill range upto almost a kilometre using 308win.