I like IT MIGHT AS WELL BE SWING the best, in spite of a horrendous "I Can't Stop Loving You" that plays to every anti-Sinatra cliche imaginable, a "Hello dolly" that comes perilously close to doing the same, and string writng/playing on a few cuts that seems "questionable" in terms of execution (but not of intent). Otherwise, though, a superb album, with the Basie band laying down a DEEP pocket that Sinatra had no problem getting into his own self.
SANDS has quite a few ardent fans, but I'm not one of them, although the band is in great form, and the ambiance is indeed "classic", especially the monologue. But Sinatra's voice sounds tired, and the whole presentation seems "show biz"-y in a not so good way, with the tempos being all wrong, and the interpretations by sinatra lacking the depth that he was so very capable of. Just my opinion, though. Like I said, this one has a LOT of fans.
BTW, the uncredited arranger for SINATRA/BASIE was Neil Hefti.