I'm not entirely sure what all the fuss is about, as my understanding is that this is primarily a system intended to aid construction work.
When our ground workers were laying out the site for our new house a few years ago they used a GPS Total Station. This gave three axis accuracy of better than 20mm (IIRC the accuracy was around 10 to 20mm vertically, around 1mm horizontally). These things seem to be in common use in the UK, as the surveyor who did the initial site topographical survey used an automatic tracking version, so he could walk around and do the whole survey single handedly. IIRC, as well as getting a rough position using the normal GPS signal because the Total Station is positioned on site at a fixed location when measuring, it can use the relative phase of the GPS carrier to get very much higher levels of precision.
When there was an anonymous complaint that we'd built the house too high, I borrowed a Total Station, set it up on the fixed reference nail that was still in the lane and showed the planning enforcement officer directly that the house was actually slightly lower than the max allowed. Not a hard bit of kit to use - it takes longer to level it up than it does for it to acquire an accurate position and then make an accurate 3D measurement.
Not sure why the EU needs it's own system, given that everyone else seems to manage very well using GPS (or, perhaps, GLONASS).
I guess if the US decide to turn off GPS we'd be screwed, but frankly, how likely is that?