For me (and other people) having your players go to a URL to get the sounds is difficult. Some of them don’t do it or they do it and accidentally close the browser. If you can count on your players to keep the Web Player open, the new Web Player is better!
If you use Discord, then all players have to get in Discord to voice chat, they are a captive audience at that point, so piping the sound through a bot in Discord ensures they all hear it. By using a Bot you also have the high quality sound that you wouldn’t get if you just sent it directly through to Discord yourself.
Also I have players in the US Mainland and some in Puerto Rico, those further away have latency on the Web Player and hear sounds after / lagged from others. In Discord they get the sounds the same time as everyone else. But, to put it into perspective the Web Player would be playing high quality for everyone, and Discord realizes there is latency and problems with someone it downgrades the audio (bitrate) so they don’t hear it in amazing quality as everyone else but they hear it at the same time.
The Web Player that Syrinscape provides is full quality audio and still the best thing to use, but Discord Bot is an option for various reasons.