Kysely is a little more established than Drizzle, which I think is one of the major reason why it has broader adoption. My bet is that Drizzle is moving really fast, gaining adoption, and might catch up at some point. It's also - in terms of performance - super fast, and nicely layers on top of fast database clients.
Some of the differences that I liked about Drizzle were the extra database drivers being core and developed as part of the main project. It supports prepared statements, which is awesome. The Drizzle API also covers an impressive percentage of what you can do in raw SQL, and when there's something missing, like a special column type, it's been pretty straightforward to add.
I prefer the way that it lets us write parts of queries, and compose them - like you import expressions like "and" and "eq" and you can write and(eq(users.id, 'x'), eq(users.name, 'Tom')) and you can actually stringify that to the SQL it generates. Or you can do a custom bit of SQL and use the names of table columns in that, like `COUNT(${users.name})`. I can't say scientifically that this is superior, and it's almost a little weird, but I've really found it a nice way to compose and debug queries.
That said, Kysely is also a great project and it'd be possible to build great products with it, too. I just found the momentum, API, and philosophy of Drizzle to be pretty compelling.