The 6.8 SPC will fit in a standard AR-15. The .308 Winchester/7.62mm NATO requires a longer magazine well to accommodate the longer round which is the AR-10. If you have a multicaliber AR-15, all you need to do is change out the upper (or barrel if you have the MGI QCB upper) and the magazine and you have a 6.8mm Rem SPC AR-15.
I own an RCBS Rockchucker, it can only reload cartridges that will fit in a standard AR-15 magazine well (COL is almost same as .223 Rem), so I'm much more apt to want to use 6.8 SPC over .308 Winchester/7.62mm NATO since I'd have to use a different press when I'm prototyping my loads. I prototype my loads in my Rockchucker then mass produce them in my Hornady Lock-N-Load AP.
The 6.8 SPC was designed to be a compromise between 5.56mm NATO and 7.62mm NATO while being usable with the AR-15/M4/M16 platform. You also get 25 rounds with 6.8 SPC. Another caliber if you like playing around with the AR-15 platform is 6.5 Grendel. There's a bit of rivalry between 6.5 Grendel and 6.8 SPC. You also can get 7.62x39mm AR-15 uppers and magazines. I think those calibers plus .223 Rem/5.56mm NATO are the best rifle calibers for the platform. Granted, there isn't much of anything that can't be put through an AR-15 these days since it's the most tricked out rifle platform out there. If it can fit in a magazine that can go into a normal AR-15 magazine well chances are someone has designed a barrel, bolt and bolt carrier for it if not a complete upper that fits on a standard AR-15 lower receiver.
One of the reasons the AR-15/M4/M16 is more popular is because if the increased capacity of the firearm over the AR-10 and M14. You only have 20 rounds for the 7.62mm NATO rifle, but 30+ for the 5.56mm NATO rifle; 40 round 5.56 AR-15 magazines are not uncommon.