I started reading the Hyperborea stories. There's also Avergoine, which is more conventional medieval, and Zothique, which takes place in the final days of the planet Earth with the last few remnants of humanity awaiting their end. Hyperborea is set on Greenland before the Ice Age.
And the family resemblance to Sword & Sorcery is very clearly visible. Smith wrote the first story just a few months after Howard's first Kull story had been published in the magazine they were both writing for, so he seems to have actually picked up the idea from Howards rather than the other way around. The world is certainly very S&S and the encounters with supernatural things are also very S&S. But the structure of the stories is very different. They are not action packed adventure stories but also not mystery investigations like Lovecraft wrote. They are artistic expressions from an artist who also did a lot of poetry, painting, and sculpting. It's not about the narrative but really all about atmosphere and mood.
And yes, it's true what people say, they are also quite funny. Not as obviously comedic as Leiber's stories, but The Tale of Satampra Zeiros and The Door to Saturn are full of jokes which you probably won't all spot on the first pass. It's not people doing funny things but a certain absurdity in many sentences. The Testament of Athammaus is not a funny story, but that absurdity is still there when you're looking out for it. Things happen that are kind of funny, but only when they don't happen to you. For the protagonist they are ideed horrifying.
The Hyperborea stories are not long and there's only 10 of them, but despite Smith's extensive vocabulary, I've found them very easy to read so far. I recommend taking a look at them. Their influence on Leiber is very noticable and you can also spot the Lovecraft crossovers.