What's your priority? Larger sensor? Or more lenses in the native mount?
If you have a ton of manual focus legacy glass, particularly rangefinder lenses, you want to adapt, then the NEX makes more sense, as the APS-C sized sensor is bigger than the four-thirds one, and the crop factor isn't as extreme, making wide angle less of a PITA to acquire.
OTOH, if you have no legacy glass at all, and are building a system from the ground up, micro four-thirds (at this time) makes more sense, because of
the larger number of lenses that are available from the system being two years older and having two different companies contributing to the pool (Olympus and Panasonic).
In a few years, the lens availability difference might not be so great, especially as the 3rd party lens manufacturers kick in, but Sony hasn't had such a great track record of creating lenses for the Alpha system. And at present, the NEX e-mount system only has seven lenses in it, of which only five are readily available.
Lenses are the other half of your camera, and arguably, the one that you will spend the most money on, and that will stay with you the longest. Bodies come and go. Your glass can last you decades.
I've done a ton of manual lens adapting on my Canon EOS cameras, and I enjoy it, but I'm getting older, my eyesight's not as good as it used to be, and autofocus is just that much more convenient. I got a used Panasonic G3 kit for US$450. Used micro four-thirds bodies are
cheap. As in they can be found in the $250-$300 range if you just want to try one.
I will add one small caution, though: I was surprised to find that the sync speed on my G3 was 1/160s. This seems to be pretty standard across both NEX and mft bodies.
I would also caution you to really consider whether you want a mirrorless compact, or if a dSLR might be a better choice. When it comes to things like lighting gear, going with one of the Big Two (Canon/Nikon) is likely to give you better 3rd-party support for things like TTL-capable PocketWizards.