If money wasn't a concern, I would absolutely go with new over used because of the warranty and the reassurance that it hasn't been abused by anyone, but I think this is asking what we would do if we want/need a "good deal".
American cars definitely don't hold their value the way Hondas do, so this question is important when buying American. But personally, I won't ever buy an American car again. Even though a Honda might initially cost a little bit more than most similarly equipped comparable domestic vehicles, the maintenance and repair costs are DRASTICALLY lower in the long run (for Hondas). I had a brand new American car that was in the shop for repairs more often than three different used Hondas I've owned PUT TOGETHER, so I'm speaking from experience.
All that to say: I would go with a new Honda over a used one. It's just like someone else said above me, the difference in price between a new and a late model used Honda is usually negligible, so there's really no point in buying used when you can get a new one for almost the same price.
If a new car isn't financially feasible, then I would have to go with the newest used Honda I could find. But again, they hold their value so well that in order to find a "cheap" one, it would have to be REALLY old.
