Bistro is a definite winner in this battle - HOWEVER, it is kind of like comparing bologna to foie gras.
Bistro is the full-service, white-linen, chef-designed culinary experience. It is quite expensive compared to other options, and is not covered by the dining plan.
Chefs is the brasserie-style, casual, a la carte, simple French dining experience. It is moderately priced and is covered by the dining plan.
Bistro does not do rotisserie chicken and croque monsieurs; Chefs does not do gastriques and whole lobsters.
PP has already answered your other question (who isn't covered?) but here it is in more detail:
~Swan/Dolphin restaurants
~Anything at DTD except Captain Jack's or Wolfgang Puck's Cafe (the Dining Room is not covered) or Raglan Road or Planet Hollywood - these four TS are covered
~Victoria & Albert's
~Bistro de Paris