Semi's need to have a cartridge that chambers easily. Small base dies return the brass back to the orginal size. It all depends if your AR has a tight chamber or a lose chamber and if your dies are made to min or maximum sammi specs. RCBS makes a special small base die. Dillon Precision doesn't specifically state it, but if you call them they will tell you their dies are small base too. The reason being they market reloading eq to machine gun owners that require small base dies. I reload for several ARs, and I use Hornady dies without a hitch. I called Hornady and they said you usually won't have a problem with their dies because they ream them to .001" of SAAMI Min. Please note they said "usually wont have a problem." I've found this to be very true. As long as your dies say Full Length or FL, I would go ahead and just try them. You probably will be fine. If some rounds don't go into full battery, try another magazine. If they still don't go into battery, borrow a small base die from someone and try it out.
BTW: DPMS shows rifles with both .223 and 5.56x45 chamberings. While both the 223 and 5.56 cartridges are the same in external deminsions, they are not loaded the same. 223s are loaded to saami specs and 5.56 are loaded to Nato specs. Basically the 223s have a chamber which uses a tighter reamer and 5.56 have a loser reamer. I'm sure the 5.56 are have longer throats, and I also believe the chamber is a little bigger on the 5.56s to allow for consistent chambering of the round. This would be an important issue in combat. If this isn't confusing enough, the military uses pressure readings from the bolt face instead of the front of the chamber like saami. So you have two different measurement points,it is like comparing apples to oranges. It has been published that it is perfectly safe to use 223 in 223s and 5.56 chambered guns. However, it isn't safe to use 5.56 in 223 chambered guns. In 223 chambered guns you should only use 223. The 5.56s are loaded a little hotter, and are unsafe to use in 223s. The 5.56s keep the pressures down to safe levels because of the larger chambers and longer throats.
How do you tell if your gun is a 5.56 or 223, look on the barrel. It should be stamped on there as one of the two chamberings. There are also some variant chamberings like the Wylde chamber which allow for using the 5.56 bullet while still retaining the accuracy of the 223. I have one AR chambered in 5.56 and it shoots sub moa all day long.
The reason for this long post is if your gun is a 5.56, it probably has a loose chamber and your dies will more likely work fine. If your gun is chambered in 223, they probably will still work just fine. It is just a little more likely you may have problems.
Hope this helps
Now go take some aspirin and start reloading