Just to add a reason for my choice of New Order:
Depeche Mode found a niche that worked for them really well, and they've done a lot of excellent songs, but they kind of stick to what they're great at. New Order is more interesting to me, because they seemed to experiment with their style and sound a bit more. Blue Monday sounds very different from Age of Consent, or Crystal, or Ceremony. That gives them a bit of an edge for me.