Beehaw is still Lemmy (unless anything has changed recently), but the instance is run a particular way. There should be a link somewhere about their philosophy and what the differences are.
In terms of vibe / community, I would think that there are more differences between the individual instances than the software that they run. That’s something which is easier to get an idea of as you use it more.
When I was starting out, Kbin didn’t have as much third party support, so there wasn’t a good way to use it on mobile. That may have changed since then