I think Sony has the upper hand there, actually. Launching at the same price as the competition while simultaneously being far more powerful means the choice will be pretty obvious for most people...
...until Nintendo drops the price of the 3DS, something they can do at their leisure (keeping in mind that, with regard to manufacture costs, Nintendo's making almost $150 on each 3DS sold) and that Sony's not going to be able to do for a long time (Vita's being sold at a major loss, with Kaz Hirai saying it's supposed to be profitable within three years).
3DS also still has a fancy gimmick as a major draw; Vita's gimmicks are the touch capabilities, which the DS had seven years ago (though that wasn't multitouch), and 3G on the more expensive model, and I think the crowd response at the Sony conference when they mentioned AT&T should sum up most people's feelings about that. Also, while both systems are backwards-compatible, it's really just a technicality for the Vita; unlike the 3DS, which can play DS cards, the Vita can only play PSN releases of PSP games, so the two dozen UMD games sitting on my desk are useless for that device. Which is a shame, because the Vita is supposed to be able to automatically remap functions in PSP games to the second analog stick without anything needing to be done on the developer's part.