My 110FP is in .308, and is superbly accurate. The question is a good one, here's my .02;
The 110 is a long action. In .308 you have about an inch of extra bolt throw. Where the extra space in the magazine would be is stock material. I am not familiar with any problems related to this.
Where this may become an issue for you is the idea of changing your rifle's caliber. Midway sells kits to swap the barrels on the 110 series to different calibers with the same cartridge head dimensions. For example, a 30/06 can become a .35 Whelen, or a 22-250 in short order with a few tools. .308 can become .243, or 358 Win, etc. It's an idea.
Ammo for the .308 is readily available at low cost, like 30/06 used to be. (Now someone will come up with an old lot of 30/06). As a reloader, this isn't an issue for me so I am not up to date on it.