Where exactly would you see the biggest differences between the Corona render I uploaded and what you expect? Added an SDS, changed the gamma of the image to what the Physical used and played a bit with the height values.
C4D natively uses Sub-polygon Displacement, which might be unique and not be found too often in other renderers.
I also guess it will be hard to get exactly the same results from both renderers.
Adding an SDS makes perfect sense to me because this is what C4D basically does with the "Round Geometry" option. The manual says to this option: "Since SPD cannot calculate a normal Phong shading when it is applied, a special algorithm similar to that of the Subdivision Surface is used to ensure that the object is rounded before the SPD is rendered."
I agree, though, that some options the C4D displacement has, would come in handy sometimes, so I would not mind having these within Corona (actually everything ;)).
CU
Michael