Break it down:
Basic Section:
Convenience:
-Apples. No peeling necessary, seeds are confined to the core.
Hardiness/Transport:
-Oranges. Peel protects. However, apples are no slouch either; oranges' advantage here is not as great as it would be in a oranges vs. peaches debate.
Availability:
-Apples. By a lot. Pretty much guaranteed year round, with little variance throughout the year.
Straight Maximal Taste
-Oranges. Probably a straight-up better taste.
Better Minimal Taste
-Apples. You can get a mealy apple, but not as frequently as you get a completely icky tasting orange.
Variety
-Apples. You can consciously choose sweet vs. tart vs. crisp vs. soft defending on mood/use. Oranges, you just hope and pray.
Legends
-Apples. Johnny Appleseed vs...
Rhyming
-Apples. In a landslide.
Songs
-Apples. "Scrapple from the Apple." "Bonita Applebaum."
Famous sayings
-Apples. "An apple a day..."
Colors
-Orange. Obviously.
Culinary Section
Better Breakfast
-Apples. Apple Cider Donuts, anybody?
Better Bread Spread
-Apples. Apple butter (homemade of course) kills almost any other spread, including orange marmalade.
Better Salad
-Apples. Both can augment a standard salad with greens, nuts and cheese with either apple or orange slices. However, I've had some fantastic chicken salads with apple chunks, as well as the fact that one of the most famous named salads (Waldorf salad) features apples as a required ingredient.
Better Side
-Apples. Pork chops and applesauce, anyone? I'm not sure i've seen oranges as a side.
Better Entree Usage
-Oranges. I've had pork with apple involved, but I'm hard pressed to think of other ones off the top of my head. I'm sure i've had chicken along the way cooked with apples or an apple sauce, but i'm not sure. Oranges, however...highly used in asian food (as a flavoring with duck, in some fantastic beef stir fries, etc.). Additionally, it is frequently used with great success with seafood; i think most recently i've had scallops with an orange-reduction glaze.
Better Sandwich
-Apples. Chicken salad, thin sliced green apple, some walnuts, arugula, red onion, plus or minus a little bacon, with melted extra sharp cheddar or brie cheese (quite different, but both work depending on your mood), all then grilled...wow.
Better Dessert
-Apples. I have to say. Though at maximal effect, it's just about even. Specifically, I've had a couple very very good mousses featuring chocolate with orange...in fact, any time i actually see "chocolate orange mousse" on the menu, i have to get it because it has the potential to be so good. However, with the multitude of apple crisps, baked apples, and fantastic home-made apple pies around, it just has to be apples.
Non-Alcoholic Drink
-Apples. Cider vs. Orange Juice = No contest.
Warming Drink
-Apples. Mulled spiced hot cider with a little rum after a day of skiing? Orange doesn't even attempt a challenge.
Alcoholic drink
-Oranges. Tequila sunrise, screwdriver, brass monkey, etc. vs. appletini?
Final Verdict:
-Apples. Although, on a given day, an "Iron Chef" with oranges as the key ingredient could certainly beat a meal with apple as the key ingredient; however, over the long haul and overall Apples win.