The BrowserGet function allows you to discern the browser in which it is running with moderately reasonable certainty - at least as of this writing.
The IDs it returns are as follows:
Unknown | 0 |
Chrome | 1 |
Chromium | 2 |
Edge | 4 |
IE | 8 |
Safari | 16 |
Opera | 32 |
Firefox / Waterfox | 64 |