As of Feb 15, 2020, in the top free iOS Apps under "Social Networking" category, Discord is at #4 and Clubhouse is at #6.
(It should be noted that Clubhouse is only available on iOS right now whereas Discord is a multi-device, multi-platform app. This question, for the sake of simplicity and verifiability, deals only with the iOS ranking.)
When (if at all) will Clubhouse surpass Discord in US Apple App Store?
The ranking of Clubhouse in the US App Store for iOS is higher than that of Discord.