The biggest difference between the G600 and the DeathAdder, is that the G600 is an MMO mouse, and the Deathadder is an FPS mouse.
The G600 has 12 programmable buttons on the side for your thumbs, and I see an additional two more, right under the scroll wheel.
The Deathadder has noticeably less programmable buttons.
Both are playable for FPS, and some people use the thumb pad on the G600 to map out their weapons and what not for their games, but generally, the Deathadder is known as an FPS mouse, and the G600 is known as an MMO mouse.
If you could get the deathadder 2013 at 50bucks, and you're mostly playing FPS, it might be worth it far more than the G600. I seem to see it #1 on most gaming mice rankings of 2013. But some people don't like razor because their products are just over-priced.
From what I hear and read, they're both good mice, and you shouldn't be disappointed either path you take. If possible, feel how they feel in your hands and choose which one's more comfortable.
You should also check out the G400s and the G500s. They're logitech's FPS mouse.
Not as flashy as razer, but it's quality stuff for the price.
PS: Check out the G600s as well. It's an updated version of the G600.