I purchased this camera for the purpose of having a great travel camera, and a "go to" camera when I don’t feel like lugging along a lot of equipment.
The image quality is superb, and it compares really well to the D5300, which was another camera I was considering. Where the D3300 really excels over the 3100 & 3200 is the ISO range. It takes beautiful shots in lower natural lighting situations, but realize that the lens has something to do with this as well.
There were some complaints about the camera, but again, I believe this to be due to the limitations of the included lens(which has a limited range of aperture & depth of field). The settings on the camera can only go so far as the lens allows. It would be best to match your lens with the type(s) of photography you like to do rather than expecting the camera to work like a point and shoot.
As far as the image processing and video it is on par with the D5300. It’s very easy to use, and would be a perfect entry level camera for the anyone not familiar with DSLRs. There are tons of features with this camera, and some interesting modes for certain effects that are quite simply fun & easy for anyone to use. I really appreciate the self cleaning mechanism within the camera(called the dust reduction system) that’s handy for me when traveling. If you’d like the ease of a point and shoot camera yet want much more professional looking and beautiful images, this is the camera for you.