It has greater range and accuracy, and less randomness in recoil.
The difference between the DPS might seem a lot, but 17 damage is extremely awkward:
The Shar-C kills the target (from max HP) in the same amount of bullets, except for Phoenix and Rhino.
Also, with the full fall-off applied, both deal 11 dmg.
The difference in their fire-rate is merely 3%, so it's safe to say their TTK is pretty similar.
So: Is my interpretation of the data correct (haven't tried the Shar-C yet), or is there something important I missed?