Groff Conklin's first anthology was published the same year as Adventures in Time and Space and was nearly as popular, ranking on polls of best SF books in 1949 and 1952. SFE notes under Groff Conklin that Adventures was contracted first and so had first dibs of material; Conklin could not use any of those stories for his book.
Conklin followed this with three other big compilations, and then several dozen theme anthologies through the 1950s and 1960s.
William G. Contento's Locus Index to Science Fiction notes that the Nelson Bond story is mis-attributed to Donald Wandrei on the table of contents of the first edition.