If you want a kill shot from any angle including hard quartering, it's penetration that you need, not diameter. That has to do with bullet choice more than anything, and sectional density. The "small" 6.5's and 7mm's with proper bullet choice will penetrate just as deep or deeper than the 30 cal's when you're talking about similar energy, etc.
If you're talking about real world experiences, a doe I took last year was a very hard quartering away at about 200 yards using factory 140gr remington core-lokt 7-08 out of a 20 inch barrel. The bullet penetrated about 26 inches through the animal and smashed a 3 inch wide hole through the ribs on exit, then continued on ricocheting off a boulder with a loud enough sound that I thought I missed at first. That was with a cup-and-core bullet, and it's generally accepted that the monolithic solids penetrate significantly deeper than the traditional bullets.
When people advocate using a 7mm-08 on moose or elk, they are usually doing so assuming a well constructed 160gr bullet, or a 140gr monolithic like the tsx. Having seen the performance first hand, I would not hesitate to use a 140gr tsx on moose or elk. My friend who I was hunting with at the time, has worked as a moose guide for several seasons and his personal choice is 308, and when he saw the cup-and-core performance he said "that's a moose gun".
A few people have said it already, that these two cartridges are so close you're splitting hairs. I agree the 308 is a better moose/elk choice, but the original OP post specifically stated a "deer" gun, not a "moose" gun. How did this move from a deer gun discussion to a moose gun discussion anyways? And as I said although the 308 would probably be a little better for moose, I would never hesitate to use the 7-08 with proper bullet choices.
If you're going to reload, I chose the 7-08 for the same reasons that I and many other people have stated, and especially for deer or similar size game.
If you don't reload, I would choose the 308 because finding ammunition in a pinch is worth it just in case.
I really can't put it any more simply than that. So close, it doesn't really matter... but you can't bash either one as a result because there isn't enough difference!
Red