A few months back I advised my father in law to buy a Sony NEX 3n, which we found for, at the time, an amazing deal of $299 with the 16-50mm power zoom lens. He loved it, but it unfortunately was dropped lens first onto something hard, and the lens wasn't fixable. It turned out that it was cheaper to buy a whole new kit than buy the lens, which is what he did, so I ended up with the Sony NEX 3n body.
It has though given me a chance to try them both out side by side, an interesting comparison given that they have the same sensor. However, the do differ; the 5n has the 900k dot touchscreen, while the NEX 5n has a 460k dot non touch screen, and it is significantly better. It also has a double hinge, unlike the 3n, which makes overhead shots much easier. The NEX3n has a built in flash and is over all a bit larger. Unfortunately the NEX 3n subscribes to the Nikon theory of haphazard fill in flash, rather than the brilliance of the Fujis.
Control wise, the cameras are very similar, both lacking the wheel controls of the NEX 5t and NEX 6, though the touch screen makes it easier to navigate screens.
All in all they are pretty similar, and I think you would be hard pressed to find a better deal than a NEX 3n out there right now.