I sometimes get asked to comment about equipment. This isn't my favorite topic. There are things much more important than the insignificant differences between cameras, such as vision, creativity, being an artist, and the decisive moment. But people want new cameras, so that's what they are searching for. It doesn't seem like people really want to learn how to make better photographs.
The Nikon D3300, D5300 and Nikon D7100 are very similar DSLRs that share the same 24 megapixel APS-C sized sensor. None of them have an anti-aliasing filter (which prevents moire pattern distortion by blurring the image). The D7100 has Expeed 3, while the D3300 and D5300 have Expeed 4. The differences between Expeed 3 and Expeed 4 are minor, with a slight improvement in speed and a minor improvement in power consumption.
So you have three cameras with the same sensor, basically the same software, and the same lenses. Why would someone pick one over the others?
It is no surprise that image quality between the three cameras are nearly identical, but what may be surprising is that they are not completely identical. Interestingly, the D5300 has the best dynamic range (followed by the D7100 and then the D3300), while the D3300 has the best high-ISO performance (followed by the D5300 and then the D7100). The differences, however, are quite small.
The biggest difference between the three cameras is auto-focus. The D3300 has an 11 area system, the D5300 has a 39 area system, and the D7100 has a 51 area system. That's a pretty big difference, but I'm not convinced that it is a huge deal in real world use. The D7100 is clearly the best in this category and the D3300 is clearly the worst, but the auto-focus system on the D3300 is sufficient for most (if not all) photographers.
There are some other small differences between the three cameras. The D7100 has two memory card slots, can shoot six frames per second, and has a pentaprism viewfinder, while the D3300 and the D5300 have only one card slot, can shoot five frames per second, and have a pentamirror viewfinder. The D5300 has WiFi and GPS built in while the D3300 and the D7100 do not.
The Nikon D3300 (body only) has an MSRP of $560, the D5300 (body only) has an MSRP of $800, and the D7100 (body only) has an MSRP of $1,200. Is the D5300 $240 better than the D3300? Is the D7100 $400 better than the D5300? Is the D7100 $640 better than the D3300? In my opinion, no.
But only you can know how important auto-focus is to you, or having two memory card slots, or a pentaprism viewfinder, or WiFi and GPS. If those things are important to you, then you may find spending the extra cash well worth it.
The way that I see these three cameras is like a car. They are the same make and model car, but different trim levels. The D3300 is the base trim, the D5300 is the nicely equipped mid-level trim, and the D7100 is the well-equipped luxury trim. But they are all the same model and will accomplish the exact same thing. It is a matter of how much you want to spend and how many extras you think you need.