Q. Which should I be looking for in an AR15, a 5.56 NATO or .223 Remington chamber?
This is really a matter of the role for which you plan to use your AR. .223 Remington chambers will give you slightly better accuracy, which is important for a match or varmint rifle. Any loss of feeding and cycling reliability and the restriction against shooting military ammo isn't as important as the accuracy gains for a rifle used in these roles, because for these rifles, accuracy is everything. People who just want to plink or who plan to shoot military ammo (such as most of the cheap surplus ammo available), and especially those who may use their AR as a weapon, should choose 5.56 chambers.
Opinion: Unless you have a reason to seek out .223 Remington SAAMI spec chambers, 5.56 NATO is probably the best solution. 5.56 NATO chambers still can have outstanding accuracy and give you more flexibility in ammo selection.