Feature detection is usually the way to go. If your website / webapp depends on a particular feature, check if that specific feature exists, rather than checking for particular browsers. Browser checks are still needed in some cases, for example Safari sometimes reports that it supports particular features but it really doesn’t (or they’re so buggy to the point where they’re unusable), but that’s relatively rare.

This is tough to implement when the feature is present, but implemented wrong. Or, even worse, when it’s implemented right, but the most popular browser implements it wrong and almost everyone else follow suit for compatibility reasons, except for one that takes the stance of following standards. I know safari is notorious for this, think pale moon had those issues, too, and there are still echoes from the past from pre-chrome internet explorer, thank god it’s finally dead.