Choosing the right Duel Deck
(Full Disclosure: I've purchased a lot of the Duel Decks: Knights vs. Dragons, Venser vs. Koth, Ajani vs. Nicol Bolas, Izzet vs. Golgari and Sorin vs. Tibalt.)

If I was trying to teach a new player, I actually wouldn't use any of the Duel Decks. They are classified as 'Expert' level products by Wizards of the Coast, so they may contain a lot more complexity than a new player is ready for. The complexity comes from the actual cards in the decks and the strategies that one deck needs to use to beat the other. (Side note:  Also, if you plan on playing in Standard or collecting for it, most of the cards in the Duel Decks won't be Standard legal.)

In my experience, one of the Duel Decks is typically stronger than the other, usually to provide contrast between a fast aggro deck and a slower control or ramp deck. For example, in Knights vs. Dragons, the Knights win a LOT, because the deck is full of really strong, low casting cost creatures. The dragons are bigger and tougher, but have a much higher casting costs. The Dragons deck does have SOME ramp, but most of the time it will take a early beating before it can get established, and not recover. 

(Also in Knights versus Dragons, there's a Knight with Protection from Red. The Dragons deck has a grand total of two ways to remove this guy. One colorless burn spell and one artifact creature. If you don't drawn into those, or if you use the burn spell on something else, you've got trouble.)

The same thing happens in Ajani vs. Nicol Bolas; Ajani has a lot of strong threats that are very cheap to cast. Bolas is more of a control deck, but it's not as well built of a control deck as you could hope for. The control is spread all over the place: a couple of counters here, a couple of discard spells there, so it's not very focused on one aspect of control, and therefore weaker. Again, most games go with Ajani taking the early lead and Bolas hoping to catch up and win.

The imbalance in the Duel Decks could lead to very frustrating games, especially for a new player. That could be mitigated by having the players switch decks, but all in all, they are likely to see that one deck is stronger than the other and wonder why the weaker deck is there at all.

In short, Duel Decks are great for experienced collectors and veteran players, but not so hot for new players. What you should try is....

If you are trying to have them learn the game from square one, a Booster Battle Pack is the way to go. A Booster Battle Pack has 40 cards total. Those are split by color into 5 lands and 5 other cards. The colors that you get are randomized, so you might get one that includes Red, Black, White and Blue, but no Green. You select two of the colors and then have a deck of 20 cards that you use to play a short game.

The small deck size helps a new player to get to playing the game right away, without a bunch of rules explanations. Once you've played several games, you can swap around the colors and try different combinations. The Booster Battle Pack also contains two actual booster packs, that you can crack open and add to your decks.

I used Booster Battle Packs to teach my fiancee how to play and she's really enjoyed it. For Magic Veterans, it seems like a useless product because of the simplicity, but you'd be surprised at how much fun the (mini) games can be.

Once your player understands the fundamentals of the game, have them play someone else's decks until they get a good idea of which deck archetype they like. (Aggro, Control, Combo, etc.) That way, the new player doesn't have to invest any money, but still gets to try out a range of different decks. Or, you could have the other players sit down and donate cards from their collections to build a deck of them.