The Sony NEX-7 is a popular compact interchangeable-lens digital camera while the Nikon D3200 is a soon-to-be DSLR. These two cameras are much different, but they do have one thing in common: the same 24 megapixel APS-C sized Sony sensor.
Since they both have the exact same sensor, it is logical that if one is considering the NEX-7, they might also be considering the D3200, and vice versa. So let's take a look.
With digital cameras there are three important factors: the sensor, the software and the lens. Now forget all of the bells and whistles and marketing nonsense--those things come after what is truly important (sensor, software, lens). What you are truly interested in is actual image quality. How do the photographs look? Extra features don't add to that. Yes, they can make "getting the shot" slightly easier sometimes, but they don't contribute to the quality of the final print.
The Sony NEX-7 and the Nikon D3200 have the same sensor, so neither camera has an advantage here. They're both the same, just in different bodies.
Software is next, and Nikon has the advantage. The D3200 has built-in Expeed 3, which is arguably the best software found in any digital camera. There is no argument that Expeed 3 is better than Sony's software. What this means is that Nikon can maximize the data from the sensor better than Sony can. The differences won't be significant, but you'll see less noise, more details and more accurate colors from the D3200 with a close study (the key words being "close study").
Lenses are where the D3200 really has an advantage over the NEX-7. Nikon has a large selection of high quality lenses that you can purchase. Sony has a small selection of not-bad-but-not-great lenses that you can purchase. Nikon's 18-55mm kit lens is a little better than Sony's 18-55mm kit lens. Lenses are just as important as the camera body, and Nikon is the clear winner here, both in quality and quantity.
One advantage the NEX-7 has over the D3200 is size and weight. The NEX-7 is much smaller, and, with a "pancake" lens, can even fit in a large pocket. If you are strictly looking for a compact camera with a powerful punch, you are not even considering the D3200. You are only comparing these cameras if you are interested in high resolution images for less money than what a full-frame DSLR will cost you.
Perhaps the biggest reason one might choose the D3200 over the NEX-7 is the cost. Supply has caught up to demand, and the Sony NEX-7 can finally be had for the MSRP of $1,350 (with a lens)--for a little while you couldn't find one for less than $1,800. The D3200 has an MSRP of only $700, which means you get better image quality than the NEX-7 for half the cost. Talk about a deal!
Again, if you are strictly looking for a compact camera, you would not choose the D3200. If you are looking for a compact camera but the NEX-7 is out of your budget (or if you just feel it's overpriced), consider the Samsung NX200. If you are looking for a digital camera with a lot of value that can deliver high quality images, the D3200 might just be what you are looking for.