I have several of each caliber. It's hard to go wrong with either one.
My main deer rifle is a Browing A-Bolt Composite Stalker 7mm Rem Mag w/ BOSS. I bought one when I was 18, 8 years ago, but it got stolen in 2008, and I recently bought another one identical to it for hunting, since all my other rifles are heavy-barreled and bulky guns. The Browning is lightweight and I can carry it without noticing it being there so much, compared to the others.
Anyway, back to your question....I love the .308 caliber, and it is an EXCELLENT whitetail caliber for sub-500 yard shots. The trajectory is not as flat as the 7mm Mag, but it is just as capable and quite effective, if you get some nice handloads shooting some Nosler 165gr Accubonds. If you were shooting the Accubond 165gr's out of your 308, and sighting in at 100 yards, you'd be 13.8" low at 300, and 56.6" low at 500.
I prefer the 7mm Rem Mag b/c of it's very flat trajectory and how I can sight dead on at 100 yards, and only be about 10.7" low at 300 yards, and about 44.0" low at 500 yards. It tends to make shooting easier, especially if you don't carry a range finder with you.
It's not a huge variation in drop between the 2 inside of 500, but noticeable enough.
With that being said, if you want a flat-shooting lazer gun that is 100% perfect for whitetail hunting....Look into a Weatherby .257 Weatherby Mag.
Zero dope @ 100 yards, 8.0" low at 300, and only 34.9" low at 500.
I love my Mark-V Accumark .257 Wby Mag, and have taken several deer with it, using the Weatherby brand ammo, loaded with 110gr Nosler Accubonds. It ruins virtually no meat, with a tiny entrance and exit wound, but will totally wreck the lungs, heart, etc!