One thing to think about when shooting the .223 is the ogive (profile) of the bullet. Commercial sporting rifles usually have a different leade at the throat of the rifling than military arms. The FMJ bullets designed for use in military arms are designed to properly engage the longer leade in military rifles barrels. The FMJ bullets I refer to here are those usually sold in bulk and made by RP or WW There are commercial FMJ bullets, such as those made by Sierra for instance, that will work fine in commercial sporting arms because the profile is designed for them. Soft point or HP bullets, no problem, because this bullet type is not normally made for the military 5.56mm. This same comment applies to .222 Rem. as well.
To carry this to the specific question of the OPer, some of the inexpensive generic .223 ammo may be loaded with FMJ military profile bullets, and this may affect your accuracy.