Full Screen view gives me a limited display area the size of the Window view, with the rest of the space blacked out (like a letterboxed movie). For example, if my Window view is 1880x1007; Full Screen keeps that same desktop resolution with the remaining space blacked out. If my Window view is 1680x1050, it also keeps that resolution -- it does not automatically change resolution to match 1920x1080 native.
EDIT: Fixed! I reinstalled Parallels Tools and now 1920x1080 is offered as a display resolution. I guess the monitor needs to be attached at the time of tools install for the driver to offer the correct native resolution.