So many cal. will kill a deer dead in its tracks no one can say which is right for you with the info posted.
We need more info. Like what ranges do you normally see deer at? see 300 yards much?
Just in case you all didn't know the 7mm-08 is based off of the .308 case, its just been necked down to accept a 7mm bullet. because of that the 7mm will shoot farther out with a flatter trajectory. Thin bullets mean better drag coefficient which means flatter trajectory's but fat/short bullets will transfer their energy better. I.E. they kill better.
The .338 Federal is also based on the .308 win. but they went the other way. If I have a spot to hunt that didn't ever see ranges over 200 yards I would take the .338 Federal because its fatter bullet will do more damage than a thinner bullet of the same design and weight and we don't have to worry about long range shots so its perfect there.
All three could be used out to 300 yards and kill deer reliably, you will have to be more precise in your hold over with .338 where as 7mm08 will be a laser. Take your pick all three are deer slayers.