No, there are many Vertical Kilometre courses around Europe (and a few in North America). This year a Vertical Kilometre World Circuit has been introduced, including 17 races:
http://www.vkworldcircuit.com . But the course at Fully has consistently been the fastest one for many years.
You are right that it depends on the angle of the course. The course at Fully is the second steepest in the world (1000m vertical in 1920m horizontal). The steepest is Le Grand Serre in France (1000m vertical in 1811m horizontal), where Kilian Jornet holds the course record of 30m25s. I think the path at Fully is easier than the grassy hillside at Le Grand Serre.
The usual stipulation is that the 1000m climb should be within 5km horizontal, so climbing from Aber to Carnedd Llewelyn doesn't qualify. The only place in the UK outside Scotland where you can do a Vertical Kilometre is the Watkin Path up Snowdon (the Llanberis path is about 20 metres short of height, and too long horizontally). Anyone fancy organising a Watkin 1000 race?