By the counts I carry, Goh is already getting close to Ash about Pokemon captured. (Which, by the way, is embarrassing that Goh has practically reached in one single season almost as many captures as Ash has done through all the series)
+ Goh officially has more Pokemon' species than Ash between Oak's Lab, Kukui's home and his current team.
+ Goh already has Pokemon of almost any type, while Ash took him DECADES to finally capture a Ghost Type (Gengar). He's only lacking Steel Types for now, although he could get one if either Scyther or Pineco evolve to Scizor or Forretress.
+ About number of Pokemon, Goh still hasn't reached Ash's current numbers, if we count his Tauros' herd of 30 indivuduals. However, Goh already has several repeated Pokemon: Dustox, Flabebe (one of each flower), Magikarp (although the giant one will surely evolve to Gyarados) and Exeggutor (even if each one is a Regional Form).
As far as I see, when Goh reachs Ash's numbers, I believe Ash will start to capture more Pokemon too. (Not that this is a competition, but it bugs me how quickly Goh captures so many Pokemon while Ash took years to do it). So, I believe Ash's numbers should be start to rise soon, either by new captures or old Pokemon returning (like Greninja).