Just flash the zip file. It will replace the other superuser apps. From the looks of it this is going to be the ultimate su app. Chainsdd's Superuser has been the standard till recently where it hasn't kept up with other development. There are quite a few technical issues with it and changes don't merge often to its source. It's quite slow in granting su rights for one (in all the JB ROMs I've tried). Problems with Superuser were the reason Chainfire made SuperSU, but unlike Superuser, it is closed source. It also doesn't look very nice in my opinion. Various shortcomings of both apps are the reason +Koushik Dutta
decided to make his own Superuser app. The main features of this are that it is completely free, performance well, includes all the features the other apps include in their paid versions and more, and has a much more aesthetic UI.
Also, you shouldn't have more than one su app. The reason you have both Superuser and SuperSU is because Superuser came with your ROM (system app) while you download SuperSU from Play Store (user app). Remove the user app (SuperSU) and flash this zip. It will replace the system app (Superuser).