I make three observations -
(i) We differentiate between imaginative and realistic fiction and place both Anderson and Lovecraft in the former category. Of course, Anderson wrote both realistically and imaginatively. Nevertheless, there is a clear distinction between merely realistic fiction on the one hand and fantasy or sf on the other. Anderson wrote realistic historical and detective fiction but is mainly known for his sf and fantasy.
(ii) Anderson could have turned his hand to Lovecraftian horror as to anything else and would probably have surpassed the original.
(iii) Lovecraft is known only for horror whereas Anderson's range of subject matters and genres is wider and deeper than the merely horrific.