Cycles and Eevee don't agree, and I think Cycles' implementation of the bump node is wrong. Where do I go to report this?
This is why I think so:
I made a tool that "carves" a bump map I want to use. The shape is like a V, it's a linear gradient from black to white. Imagine it like a tool bit. See example:
But now I try to use nodes to soften this shape, to ease into the transition, and give it rounded edges, like so:
To do so, I transform the bump map with a curve (I've tried vector and RGB curves, they behave about the same). The result is hard to achieve and shows aliasing, but looks OK in Eevee, see here:
Now compare this to Cycles, where it doesn't work:
No matter what I do, I can't get the peaks and valleys to curve smoothly like I can in Eevee.
Here with a much lower bump value, the sides are still much more straight than expected:
Interestingly, at lower bump values the difference between Eevee and Cycles disappears.
If you want to try this yourself, here's the 16-bit grayscale Tiff: out-cone511d.tif