When you say "full screen", I'm assuming you're referring to the full screen button on the top right of a window, as opposed to the "expand" green button on the top left of a window.
Mavericks has "solved" the multi-monitor issue by allowing multiple and independent spaces on each monitor. In pre-Mavericks, when you move to a different space on one monitor, all other monitors follow. In Mavericks, they are independent, meaning you can move each monitor to different spaces without affecting the others.
In relation to full screen apps:
- Pre-Mavericks, going full screen would move one monitor to full screen and all other displays to a black/empty/useless space.
- In Mavericks, all other monitors remain independent and free to access any of their spaces (allowing those monitors to remain useful).
So in response to your question
Full screening an application on one monitor has no affect on the others, and full screening it on your mac mini screen, should not make the app go full screen on your 27'' screen.
When you maximize a window on one screen, and then drag it to another monitor, TextEdit does not resize itself to fill the screen (whether it be to shrink when going from your 27" to your 13", or grow, going to your 13" to 27")
Overall I'm a little confused about your frustrations, but you cannot make it so a window grows proportionally based on the monitor. What I mean by this is that you cannot make it so if you have TextEdit open on your 13", and it covers 60% of that monitor, when you drag it over to the 27", TextEdit won't automatically appear as taking 60% of the 27" monitor. It will appear as the same size it was on the monitor you're dragging it from.
There are multiple 3rd party apps that help you manage and arrange your windows in Mac OS X that may help you. But as far as I am understanding, none that will help your issue, if you're referring to the top right full screen button.
You can use apps to help magazine your windows:
You may like Moom the best, and it is described: Do you spend a lot of time moving and zooming windows, so you can better see and work with all the content on your Mac? Instead of doing that work yourself, let Moom handle the task for you.