The short version is that X11 and VNC serve different purposes, so you'd use them in different circumstances.
It is possible to open a full X11 desktop remotely, using XDMCP; this is how old X11 terminals work (a central system provides the desktops and hosts all the applications, the terminals only display them). But as far as I'm aware you can't connect remotely to an existing X11 desktop.
What you can do with X11 is have a local desktop and display remote applications on it, without a remote desktop. (This might be close to what you're thinking of with transparent management of fused local and remote desktops.)
VNC's main advantage is that it's cross-platform, so you can view a Windows desktop on an X11 system etc. There are VNC servers available which allow a VNC client to connect to an existing X11 desktop, so you can re-connect remotely to your existing desktop without restarting everything. You can also share a desktop: local and remote users can use (or at least, view) the same desktop simultaneously.
As far as overhead is concerned, plain VNC is less efficient than X11: VNC transfers pixel updates, whereas X11 transfers graphical primitives (e.g. "draw a rectangle", "print this text"). This is less relevant nowadays since for example most text updates in X11 are now pixel-based.