The biggest difference between the two is going to be the bullet. Hunting ammo uses bullets that are designed with maximum expansion and weight retention in mind. This means a bullet that will "mushroom" and transfer it's energy to the target, while keeping fragmentation and jacket separation to a minimum.
Sniping ammo tends to use "match" bullets who's primary goal is balance, concentricity, aerodynamics with very little consideration to expansion. They tend to have full metal jacket construction with a boat tail instead of an exposed lead tip. They tend to have thiner jackets and instead of expanding on target will either fragment or go right through it's target without expanding very much.
Match or sniping ammo also tends to use less volatile powders and primers which behave more consistently from round to round.
Using core-lokt bullets in my 7mm, I have NEVER had a deer take a step after being hit, and never had an exit wound bigger than my thumb.
Using ballistic tips, I have NEVER had a deer drop - or run less than 100 yards - unless it was spine shot.
That with about 10-12 deer shot with ballistic tips, and at least 30 with core-lokt, at distances from 60 yards to 420 yards with both. And only 2 were not within 3 inches or less from the heart - those 2 were shot in high wind, and shot back by the liver - bad wind call on my part both times. :evil:
The bullet will make a difference, despite the shot placement. It will kill, but one may require you to track a blood trail, and one won't.
Neither of the two I mentioned are match ammo, but serve as an example of how it can make a difference. I have not, yet, tried match ammo on deer. I plan to this year, but to be fair, it will be with considerable heavier bullets (168, 175, or 180) so I will still not have a fair comparison.
That said, specifically referring to "sniping" ammo, like the post originally asked, men shot with match ammo die just as dead as men shot any other ammo.