This is a very broad question. Accuracy is also a very subjective term. What might be accurate to me, may not be accurate to you. As for accuracy on the quantative side, that typically depends on the quality of the components that makeup the AR. For example, a Kreiger match barrel should be more accurate then an off the shelf chrome lined barrel. So, you need to first compare apples to apples.
As for an 16" chrome lined MRP vs. a 16" chrome lined mil spec AR, assuming that the mil spec barrel is free floated, they should be relatively similar in accuracy. Roughly 1 to 1.5 MOA accuracy. Some will be less and some will be more. Remember, a chrome lined barrel is not designed to be a tack driver. It's designed to last many thousands of rounds.
As for a 18" Stainless MRP vs. a true SPR barrel (match grade Douglas), the SPR would probably be more accurate as a general rule of thumb. The MRP barrels are believed to be made by Mike Rock. I just don't believe that they were designed to be of the same quality. That being said, my 16" Stainless MRP will shoot 3/4MOA. Some have claimed better accuracy.
Currently, you are stuck with LMT barrels since the barrel extension is propriatary. LMT has not yet released barrel extensions as an individual item to allow someone to mount a different barrel to the MRP.