I have a book re: Prince Eddy and his times--alas, I do not recall the name at this precise moment!
--and my opinion, influenced by that book, is along the lines of what Louise has said. Quite a few factors were at work here. For one thing, Eddy's mother spoiled him terribly, causing his father to be somewhat disaffected. Not a rarity in families--it happened in the case of my father and his parents! Also, he did seem to lack motivation, which would be a sign of developmental issues. Then, the contrast to George, who seemed more of a take-charge person. And Eddy's appearance--handsome but long-necked and lanky, with a languid air--didn't do much for him either! He did seem to develop the tastes of an Edwardian "rake"--but so did many other priviledged young men of the time. Probably what bothered Alix most was his diffidence and indolence. (And undoubtedly she sensed his sexual ambiguity.) In Nicholas she found a man who was obviously very attracted to her, and wanting to "do right"--but who was crying out for direction . . . hers! Prince Eddy just didn't inspire Alix as did Nicholas.
By the way, in the excellent British miniseries
Edward the King, produced in the 1980s, Eddy is portrayed by Charles Dance, who would later figure in
Jewel in the Crown and a
Rebecca remake, among other productions. Alix and Nicky also make brief appearances during their visit to Grandmama Victoria at Balmoral.