You can check out the very non-astro comparisons between the D3300 and D7000 yourself:
http://www.dpreview.com/reviews/nikon-d3300/11
It looks like the D3300 has a tad more noise but it's spread over more pixels and overall there is nothing in it really. I read and watched a lot of reviews before buying it and the consensus seemed to be that the D3300 offers the same raw performance as the D7200 but it's not as feature packed.
But features are lost on me. Just give me a sensor, exposure, aperture, focus and maybe a light meter (what luxury!). Then get out of my way and let me drive my own camera while I collect some photons. Basically I'd be more than happy with a decent Praktica that has a CCD in place of where the film used to go.
I do understand the need for more features for pro photographers who need to be on and always ready to shoot, but I don't like how the industry uses that to manipulate public perception and sell the same gear at hugely inflated prices. Case in point: D3300 body going for around $300; D7200 for $1200. It's basically the same camera apart from the window dressing! But maybe I'm wrong and someone more knowledgeable will put me in my place. I'm all ears. Don't hold back folks. It's the only way I'll learn.