I have a ring sling and a brand new Moby.
+comfortable for extended wear
+less pressure/pain from carrying baby all on one side or the other (uh, better weight distribution)
+can be worn all day, with or without baby
+versatile (with practice) carrying positions
-takes more time to put on & could be a hassle in public
-bulkier/takes up more space in diaper bag
-can look a little frumpy without a baby in it
Ring Sling Pros:
+comfortable for small baby for longer periods of time
+folds up compact (unless padded) and fits easily in diaper bag
+doubles as blanket, burp cloth, sun shade, changing pad
+easy on and off
+great for quick trips and impromtu babywearing
Ring Sling Cons:
-may cause pressure points, pain or numbness when carrying heavier baby for long periods
-slips off shoulder when baby's not in it
-limited use of arms (when compared to wrap carrier)
-steeper learning curve (imo)
This is my experience with the two. I do love my ring sling, but I haven't mastered the back carry with it. I might love it more if I could get ds on my back without crushing one or both breasts. I might like it better if I had two ring slings to distribute ds's weight more evenly, but that just brings me back to a wrap style carrier. Also, I might like it if my sling had a little bit of stretch. Maybe.
Is your wrap stretchy like a UBW or Moby? Or is it more static like the Didymos? Whichever you have, you might try the other kind of wrap instead of a ring sling.