There's a lot to be said for the swipe idiom over buttons. It might seem like the physical action of a tap is quicker and easier than a swipe, but that assumption ignores Fitts's Law, or its touchscreen equivalent: the smaller a target is, the longer it will take for the user to hit it. You can do a swipe without looking, but to hit a button you have to mentally and physically position your finger, and this takes time and interrupts the flow of concentration.
Swiping is also a much richer interaction. The user can discover it by accident, and if they start a swipe without meaning to they can easily cancel it by reversing the action. Typically they can also "peek" at the next and previous items, even while looking at the current item. And of course, it uses no screen real estate at all.
However, if your users can't be relied on to know about swiping, you have to provide an alternative-- if even 1% of your users can't use the app at all, that's a failure.
Swiping might also cause accessibility problems. The action takes less motor control to perform, but also requires larger hand movements-- I wouldn't want to give detailed advice on this.
If you are aiming for a demographically broad audience, the latter two points suggest including both techniques, as Andrew suggests. But if you can justify it, I'd say go with swiping alone; it's a more elegant solution and you can use 100% of the view for content.