The 3DS has basic shaders that make it look much better than Wii games, but it ever so slightly worse than Wii in most other regards. If you compare the very slow corridor style gameplay of the above with something like WipeOut on Vita, the difference is really quite big.
Sure, the difference should be slightly less than Wii/PS3, simply because the Vita is probably further off from the PS3 than the 3DS is from Wii. That said, the Vita actually has more memory than the PS3, though again I wouldn't be surprised if most games are recommended to use 256 + 128 MB only, as the resolution of the screen is lower than PS3 so that it shouldn't need quite as much data either.
But there's no mistake - the 3DS is really still a lot less powerful than the Vita. The difference isn't even close to negligible. The Vita will be able to run most multi-platform games that also target 360 and PS3 without too much work, thanks to the power of its quad core gpu and cpu. It has more memory than either HD console, and 5 times the memory of the 3DS. Even a 'subqHD' game like Uncharted runs at 3-4x the resolution of a native 3DS game (700x480 vs 400x240 or something like that).
In other words, not really a contest? No, not in terms of hardware really. This battle, content is king, and then price, and in those areas Nintendo is very comfortable in Japan. However for the West, Vita looks like it's lining up some really good stuff.
That said, the price is still well in favor of the 3DS, at almost $100 less if you take a similar memory card for Vita (which will then run out much quicker).