Green just maximises the information viewable. Say a picture is 1024x768, it'll bump the window size of it to this size, and no more, because having it full screen would be useless.
I like full screen because I can set it to the full screen and forget about resizing anything again. The Mac maximise screen button does not always stretch to the ideal size:
1. Some web pages that use % dimensions do not size upwards to the optimal size with the maximise button, so you have to do it manually (with two separate actions - move window to top left, then drag bottom right corner out - so inefficient!).
2. Some applications require more or less screen space on different views, so you maximise the window and its fine, but then you get to a larger view and you have to hit maximise again.
I've only been using a Mac for 2 days and I've come across both these issues.
I've only been using right click on 2-finger tap for a couple of hours and I already love that.