You asked about advantages of one over the other. The Range Officer will come out fit better, have a better trigger, and be more accurate. Now, as to other features that are largely a matter of personal preference:
Fixed vs adjustable sights -- fixed sights are usually better for carry but I can remember when a whole lot of folks carried revolvers with adjustable sights. I don't think it's a huge negative. On the other hand, I had a Mil-Spec that shot so low I could hardly keep it on paper at ten yards!
Grip safety and main spring housing -- Most like the one on the RO better. The "beaver tail" grip safety and flat main spring housing allow for a higher hold which aids in controlability. However, some like the "duck bill" and like the arched mainspring housing. It's personal choice. People with big hands sometimes suffer from "hammer bite" because of the combination of the grip safety and spur hammer on the MilSpec. Hammer bite is where the hammer spur just hits the web of your hand between thumb and finger.
Safety --The Mil-Spec has a smaller safety which is consistent with the military style safety "back in the day." The RO has a somewhat extended size safety which makes it easier/faster to flip on and off.
Trigger -- The trigger on the RO is longer. This is a personal choice. Most with average or larger hands probably prefer the longer trigger. As I mentioned before, the trigger should be lighter and crisper on the RO (a good thing).
Bottom line, I would recommend the RO over the Mil-Spec. I have a couple of 1911s similar to the Mil-Spec just for variety. I mostly have 1911s more similar to the RO.