This is purely a personal opinion, but having visited the Dordogne and the Ardeche regions, the Ardeche wins hands down for me. Very similar areas really, but the Ardeche is less 'spoilt', with less tourists (particularly Brits) and scenery just as good.
Personally we also prefer the cuisine of the Ardeche, but I suppose if you like Duck or Foie Gras, then the Dordogne is for you!
Like I say, just my opinion, not expecting everyone to agree!