Apart from what has already been said (politics, basic UI) there are a couple more things worth mentioning:
Kbin's interface is muuuch more customizable than lemmy's: browsing form a web browser (desktop or mobile) let's you modify your viewing experience as much as any mobile app for lemmy (but lemmly itself doesn't). From infinite scrolling vs pages to font sizes and such.
kbin allows for (mastodon-like) boosting of posts, which is like a super-upvote that lemmy just doesn't have.
on kbin you can subscribe to mastodon users aka federate with mastodon. Something that lemmy also can't.
Other than that only personal taste matters in the end, and both federate with eachother, so enjoy it from wherever you are.
Kbin does a better job of putting new posts in front of you even before you have subscribed to anything, so I think it is easier to find interesting things to read. Kbin is newer than Lemmy, so Lemmy had the advantage in familiarity for people. More people had heard of it when Reddit's API drama blew up and that gave Lemmy a distinct advantage when people picked a new platform. Kbin also has some annoyances like not being able to collapse comments and vote buttons being at the top instead of the bottom of posts and comments. If someone has written a lengthy comment, I want to read through the whole thing before I decide how to vote and I don't want to scroll back up to get to a vote button. To reply to a post you also have to scroll through the comment section. In some cases it's good to see if someone else has already said what you are going to say, but in other cases if someone is looking for personal stories, you don't necessarily need to read everyone else's story before submitting your own.
Personally I have this kbin account and a lemmy account as well. My Lemmy server seems to go down more often and the default sort always shows the same days old pinned posts from my server admin that I can't seem to hide after reading. On Reddit, I didn't have to switch sort to see newer stuff so Lemmy comes across as pretty stale sometimes even though there is a fair amount of posting going on.
Kbin's UI is just better. I realize both can be customized, but I'd prefer not to mess around with any of that yet. Plus I know people on mastadon, so that sealed it for me.
I have a kbin account which I switch to everytime lemmy.world goes down and the only real advantages I see are the better UI and the integrated microblog thing. It's basically Lemmy and Mastodon wrapped up in a single piece of software.
I think kbin is more promising than lemmy. The admin seems a good guy, kind and levelheaded. Since a month ago, before the blackout, he build kbin by himself and since then someone even volunteered to help him polishing the site.
The site looks polished but still in beta and they're actively ironing out hundreds bugs and feature request by us users.
Ultimately also the users are nice people. Many of us have donated money and right now the admin have enough money for nearly a year. Source: https://kbin.social/m/kbinMeta/t/177112/kbin-project-management-costs-financing-future-plans
Kbin has a way better UI, but it needs better servers and having apps for Lemmy like liftoff makes me wait to get something similar before switching back to kbin.
I like the UI better, like that it interacts with things like Mastadon, and, what was honestly the biggest thing, doesn't have a dumb auto-refresh I can't disable (which Lemmy did (at least for a while)).
They both have a lot of growing up to do. Not being able to collapse threads in kbin is driving me crazy; especially for long threads with many nested levels, I can't tell what is even top-level.
Kbin also has Mastodon integration (though it's still being worked on and isn't in its final form yet), which I think is handy because I'm hoping that Kbin doesn't defederate from Meta, so that I can also still have an account to keep in touch with people I care about who are going to be using Threads without having to manage another account elsewhere.
I also prefer the layout to Kbin better. While the stock Lemmy layout is nice (it does a fantastic job of emulating the old.reddit layout), I like the fact that Kbin shows a little bit more text about each post. It also keeps more data public (like your votes and reputation scores), which I actually prefer being out in the open, as it helps weed out people who may be giving bad faith arguments in various discussions.
I like that there's both an update, downvote and boost feature. Recently the sorting / weighting mechanism was changed where boost = 2 upvotes so it's nice to upvote something + give it a boost so it sorts higher.
There's a lot of customization user wise also, I've been exceptionally busy working with the other contributors to make the mobile UI/UX a priority. There's been a heap of dev work going around so keen to see when that all gets into prod.
I've got a feeling that with another solid month or two of updates, tweaks and features that kbin will be really solid.
Literally was that Kbin started with the letter K, and thus matched with my going DE, KDE. So really just a matter of taste I guess. I always recommend people to use what they like.
I set up both, and kbin was up while I couldn't get on world for 36 hours. Granted it turns out I had to just quit the app to get it loading but I didn't know that for a couple days and kbin worked fine
On top of elements already mentioned by others, an initial draw for me was the tenor of exchanges I was seeing on kbin. Of course the instances all interflow and I won't claim that Lemmy instances are not the same. But that was my initial experience. I like having a home base where there's some effort made to be communal and give thought out answers.
I was introduced to kbin first, and after giving both kbin and lemmy a shot, I decided on kbin as my primary. I prefer the layout mostly. Yes I know you can customize lemmy to get it to a similar look and feel, but kbin feels great straight out the box. The Mastodon integration is interesting, and its nice to keep up with what's going on there at the same time on one site. Also as federation users, we are encouraged to join smaller instances to lighten the load of ml and world, and kbin seems to be a good compromise of joining a smaller instance that isn't too empty. Also, with the recent hacks happening with the bigger lemmy instances, I feel like I made the right call sticking around here.