Being a former retail professional and member of International Council of Shopping Centers. I can truthfully report that Bloomingdale's is definitely considered to be a high end luxury retailer on par with Saks, Bergdorf-Goodman, Barney's, Nordstrom, Neiman-Marcus. Lord & Taylor and Macy's have luxury designer departments (which allows them to pretend that they are high end merchants), but their designer shops don't feature clothing by the likes of Armani, Valentino, or Badgley Mischka (remember their short lived HSN collection?).
Among the bunch Bloomie's is my favorite, but that could be because of past experience. These days they are all selling the same stuff, but there used to be a time when Bloomingdale's and Barney's were the places those of us who dress a bit more avante garde or trendy would have to go for our designer duds.