I think it's hard to say for sure b/c there are so many variables (skin, structure, size, etc.) that could make one bag look more formal or not, but if I had to pick, I would say that the single-handle is a bit more dressy. Of course my immediate frame of reference is the Kelly vs. the Birkin, Bolide or Plume, but I do think that single-handle bags (excluding shoulder bags) are more formal and dressy than two handles because it's a bit more streamlined and elegant and reminds me of vintage bags. When I think of dual-handled bags I think of in terms of hand-held totes which lend themselves to more practical, casual and daily wear.