Both have advantages and disadvantages . My personal opinion would be to get the AR-10 , in .308 caliber . You could then purchase a .556 Upper at a later date , and then have both capabilities .
There are those who are enamored with the .556 , but I'm not one of them . There are those who are enamored with the AR platform . I'm not one of those people , either . Trying hard to be objective in answering this , cause frankly , I think the AR platform is the biggest POS ever devised by man-kind . Sucker's had more "EC's" done on it than the space shuttle , and still leads the world in jams , mis-fires and malfunctions . If you are getting a piston driven gun , similar to a AK / SKS , then good on ya .
Don't recommend a gas impingement system , though . Like a high maintenance woman ...
The AR-10"s seem to have less headaches ; even in the gas impingement system guns , due to the larger caliber cartridge recycling the system .
Carried a M-16 for four and a half months in Nam , and when the third one jammed in the same fire-fight , I was lucky enough to have a SKS within reach ....I still have the SKS . I'd use a AR platform gun , if forced to . Until I could replace it with something I'd trust my life on .
That's my opinion . Hope it doesn't ruffle to many feathers in the "God Gun" crowd .