I've got both, and shot big deer with both. Both performed well.
I've vowed that my last 30-06 was my last. I've got 8. I really don't need another.
308 WIN? Look, I've only got one. Currently. I've got waaay more brass than that. I'll probably buy another 308 WIN when I can figure out a niche to fill. I'm also going to have grandchildren coming on line. Probably a 308 WIN will be in my future just so I have something to pass along.
In general, I would say that for an average whitetail deer hunter, both will work nearly interchangeably. I prefer 30-06 for my longer venues and 308 WIN for the shorter.