Since I've started to use Corona I've always had the impression that were something wrong about bump mapping, in particular a flatter look compared to other renderer.
Now I've discovered this, using Cinema4d noise gives proper bump(I've also added a checker shader on it just to be sure to get the proper scale), using the same noise baked into a texture(first image) and used instead of the native noise gives a totally different look and a way flatter bump mapping(a thing I noticed with every shader I've builded).
I've tested the same situation on other engines and work as expected so it should be an error with Corona bump.
If that's the case it's a big issue and should be solved ASAP.
I'm on OSX 10.11.3, C4d R20 latest Corona beta version, if needed I can provide a scene.