Part of the reason why I think both subjects work so well as pastiches is because there’s a lot of room to work with. Which is obvious with the Cthulhu mythos. Compare The Strange High House in the Mist with At the Mountains of Madness. Just in Lovecraft alone, there was a wide spectrum of stories and tones. Even in his own life, his circle of friends like Clark Ashton Smith and Robert E Howard worked with elements of his ideas.
It seems a little stranger with Sherlock Holmes can inspire such a wide variety of work that, well, isn’t a train wreck. I mean, the character inspired a genre but all the stories are about two guys, Holmes and Watson. That’s a lot more limited.
I think the secret to Sherlock Holmes being open such a wide variety of interpretations and still being ‘true’ and entertaining is that the character in the original stories is pretty flat and distant. Which isn’t a dig because the original stories were driven by plot and some really good plots at that.
In comparison, Hercule Poirot has a much more defined personality and would be much harder to write about good pastiches about. Holmes is enough of a cypher that Basil Rathbone, Jeremy Brett, Robert Downey Jr. and Benedict Cumberbatch all play very different Holmes that all still work.
The author who straddled both pastiches was, of course, August Derleth. While I appreciate that he kept Lovecraft in print enough to become a part of culture, he really didn’t capture the cosmic despair of Lovecraft. On the other hand, his Solar Pons stories, openly pastiches of Holmes, are a lot of fun and frankly much better written.
These pastiches are almost a guilty pleasure for me except that I don’t think there’s anything to feel guilty about.