Depends which Aubrey is vs Sparrow. Like if you take young Aubrey on the Sophie, Sparrow might have the upper hand since the Jacks crew was not really at its peak preformance, plus Jack though still inteligent and able, I think he might be prone to make a mistake or two.
Now, if you take older Aubrey on Surprise, this is a more fordimable opponent, although maybe not as fast as Sparrows ship, Aubrey had would you would call I think a crack frigate, every man aboard knew his duty and knew it well. Im sure Aubrey might try to cut out the Pearl in an evening raid of some sort.
Lastly, older Aubrey on Surprise/Suffolk. Aubrey still had his wits but he was getting old, after several engagements he's been hurt time and time again, even lost some of his vision. Surprise still had most of its old crew but also alot of new hands, therefore its abilities might be slightly less than what they were in comparison to the Surprise back in its height of efficiancy. Sparrow would still have a good fight ahead of him but could get out ahead. Finally on the Suffolk, the ship was not ment for speed or chaising other vessels, as long as the Pearl was able to get away from the Suffolks range or avoid being boarded at night while anchored, Sparrow would come on top.