Note 3 on OSX. Stuck in "Connected as a media device"
I am a professional Mobile Application Developer, and often use my own personal Galaxy Note 3 for test at the office, and I've never come across this issue.

When I plug my Note 3 into my Mac Pro, it appears connected as a media device, and it appears in the Eclipse "device chooser" window.

What you probably need, is the Android File Transfer software, which can be downloaded here.

If that doesn't work, try looking for Samsung drivers for OSX, although I don't believe I ever installed any.