I regularly use Microsoft Remote Desktop in full color mode over 3G from the UK against a machine hosted outside Paris, as an example of what's possible given enough effort, RDP is a bastion of pure awesomeness. I have on many occasions failed to notice I'm running gvim on the remote box compared to a local VM on my laptop. In full screen mode they're practically indiscernible if you aren't paying attention to the latency of your keystrokes. It's impressive enough that on a high bandwidth low latency connection, even small YouTube videos play well.
RDP is heavily integrated into the OS, I'm not sure where it derives its advantage, but for example, dragging a window across the desktop (requiring massive region dirtying) is somehow almost flawless. For example it might be quite an easy affair to delegate compositing and blending to the client, such that the client has a full copy of the bitmaps being dragged around the screen. VNC is intentionally stupid by design and nothing like that (it hails from an era when a microcontroller was preferable for cost reasons compared to a computer in some hypothetical X terminal design - remember VNC is from the 90s).
There is a ton of stuff Libreoffice can do this in this department to produce a compelling solution, alpha quality "release early release often" editions shouldn't be used to form a long term judgement, especially when examples of better implementations already exist, and there is real money on the table to motivate further innovation.