The browser extension is a companion app that is a great addition to the apps for Mac/Windows. The extension offers the same experience as with our desktop apps, only with a few differences:
Quick Response Shortcuts only work in the desktop app
Native apps offer a slightly faster experience
In short, you should go for the browser extension if you only plan to use your canned responses in the browser and don't want to install an app on your computer, and the native apps if you want a fully-fledged solution to manage and use your canned responses in the browser and in other apps (Slack, Word etc).