Starting with the Man from Providence himself, here's what HPL wrote to Henry Kuttner--years before Kuttner married Moore, by the way:
"[Clark Ashton Smith's] genius & style are of a highly individual sort, so that he undoubtedly ranks with Robert E. Howard--& perhaps C. L. Moore—as one of the supreme leaders of the WT [Weird Tales] group."
This is quite interesting. Depending on how you read it, it appears that Lovecraft is saying he ranks Moore above even CAS or REH. He highly respected Howard's fiction. Some of it more than others, but his high regard really isn't in doubt. The same can be said of Lovecraft's opinion of Klarkash-Ton's work, only moreso. Thus, his apparent ranking of Moore as the "supreme leader" amongst the Weird Tales stable is kind of startling.
Clark Ashton Smith was also effusive in his praise for Miss Moore. Here is what he wrote to Robert Barlow in 1934:
"C. L. Moore certainly must be a genius--I liked her 'Dust of Gods' almost better than any of the tales so far published. (...) Thanks too for giving me her address-I'd like to write her..."
I also seem to recall reading a letter from either HPL or CAS where one of them refers to her as "Queen Catherine." If I track that down, I'll post it here at the DMR blog.
When it comes to what Robert E. Howard thought of Moore, there is less surviving hard evidence. We know the two corresponded. However, none of his letters to her survive. Very little of Moore's correspondence with REH survives. We know he praised "Black God's Shadow." His admiration for the Jirel stories probably explains why he sent Moore the typescript of "Sword Woman."
We also know from Dr. I.M. Howard, Robert's father, that REH held Moore in high regard.
All of this begs the question: What was it that HPL, CAS, Bloch and others found more to their liking in Moore's tales of Jirel rather than REH's Conan stories? Something to look at another time.