Operating system: Windows 10 64 bit
Graphics card: Nvidia GTX 750 Ti
Short description of error
The UV Texture Coordinates via the Texture Coordinate Node differ in Cycles and Eevee.
In particular, in Cycles, the coordinates are just 0, if "Use UV for mapping" is disabled in the curve data.
Eevee does not care whether this checkbox is enabled or not.
Also, I think the documentation for this checkbox is wrong: The tooltip says "Use the UV values as Generated texture coordinates."
However, it does not change the Generated texture coordinates, but the UV in Cycles.
I also don't know why anyone would ever disable the checkbox, since it just results in no UVs for Cycles.
Exact steps for others to reproduce the error
Top left: UV + Use UV for Mapping
Bottom left: UV
Top right: Generated + Use UV for Mapping
Bottom right: Generated