I have hunted here in TX for over 20 yrs and have never come across a situation (within reason) while hunting whitetail, that a 7mm-08 could not handle. Yes, there are the 400 meter shots, in an arroyo, through the brush, etc., where a bigger gun might be more beneficial. However, IMHO, 7mm-08 is an excellent choice. Reasons? It fits the light-weight, short-action, low-recoil profile that makes shot placement more optimal. The Hornady 139 gr. SST is an excellent cartridge for most whitetail hunting situations here. Also, it is widely available.
Second choice... the .308 Win. I have a .308 (AR-10) I use for hunting hogs and it does quite well with any size hog I come across. It has a huge number of choices in cartridge setups. Especially if you handload. The .308 will adapt easier in that you have more options to change the variables (bullet type, weight, etc) to fit a wider set of situations. Where you live, you may want the versatility to move up or down this "scale". While in TX, you may want to increase the powder and reduce the bullet weight for this particular hunting situation. Its your call. Both are going to be around for a long, long time.
If I were to start with no rifles, I may very well stick with the .308 just on the idea of reloading simplicity. But I do love my Steyr-Mannlicher 7mm-08.