we have three days outside of Paris to explore with no agenda. Would our time be better spent in the Loire valley or Burgundy? We are outdoor people and winos who also love food.
You say you love wine and food, for that reason, Burgundy would be perfect for you. Obviously, it's also possible to find good wine and food in the Loire Valley and it's well known for its chateaux. But when I see someone say they're "winos who love food," the pointer shifts in favor of Burgundy, which is one of the two or three greatest wine areas of France. If you have follow up questions, you can ask them here and/or send me a Private Message and we can chat one-on-one discussion off the public part of the Board.
I won't try to add to what Kent said--he captured the relevant distinctions perfectly--but if you'd like other thoughts about Burgundy and what to do and see, then post your questions here as well as to Kent.
I think you can have a very satisfying time in either region in three days.