So far I've gotten the following:

GPS
  • Easier to wire
  • Requires no calibration
  • does not vary in speed due to tension on wakeboard line or multiple riders


Paddlewheel
  • Is not affected by current or wind
  • more likely to "set it and forget it"
  • relative speed is consistent and reliable


I still haven't heard anything compelling for why GPS would be better than paddlewheel (specifically for surfing). Just that people don't mind or don't experience the GPS downsides. Because all the "it just works" or "my speed stays spot on" are things I experience with my paddlewheel. My experience has been that it's just as reliable.