One thing missing from the D3300, if it matters to you, is exposure bracketing. This is apparently an advanced function, and the D3300 is targeted towards less experienced photographers. I'm sure there are other omissions as well, but I very nearly purchased a D3300 recently but like to shoot HDR, and for that I need certain features.
Image quality aside, which are all excellent, the a6000 competes more with the D5300.If you're just starting out, the real question you should be asking is what system do I want to buy into? Which has more lenses I will use and can I afford them? I've been somewhat happy with Sony-I've been an e-mount fan since the NEX-5 and back then Sony did not have many lenses for this system. There are great lenses now-not cheap though. I stick with e-mount because I travel extensively and appreciate the small size, as well as the features Sony packs into these tiny cameras. I have several e-mount lenses now, and it suits my purpose.