Thanks for looking in to this again Nikola. I have put a link in to a drop box zip with the file and oak texture so hopefully that works.
Please see the attached images. I have just used the respective material preview ball scenes with a semi gloss grey diffuse base so we can just see the bump effect but there will be some slight calibration variation in hue. Also I have use the vray default of 1cm strength and picked 58% for the corona one as a sort of half way strength. Making it more or less doesnt seem to help / make much difference.
As a side note I personally prefer the cm scale range rather than a percentage - at least you can visualise roughly the amount you are dialing in in CMs, where as percentage is quite arbitrary especially if we can go over 100%. I wonder if there could be some calibration for this between black and white in corona?
So regarding the Oak bump images; I have just made a straight desaturated with enhanced curves jpeg of an oak texture and loaded that in to the bump slot in both mat editors. Straight out of the box you can see vray picks up every strand of wood grain and you get a real sense of a rough wood surface. There is a strong shading artifact in the preview ball but I think that is the way it is set up/lit. As for the corona one we just get a high frequency noise that doesnt represent the wood grain. If I ramp up the strength to 500% we still get this strange high frequency noise, but if i blur it by 0.5% magically we then get to see the wood grain but we have sacrificed a bit of texture detail in the process and I still prefer the detail and feel of the vray one as it is more fiberous where the corona one smooths out the subtle threads due to the bluring. Also we shouldnt need to blur this texture to see it!
Moving on to the checker. I have used the same strengths as the previous test (1cm and 58%) This is a hard test case as we are going from pure black to white in a pixel width. But vray has a reasonable stab at it and there is a bit of a surface there. Corona fails to create a surface. If I then blur the checker for vray giving a ramp between colours you get a good relief and you can feel that checker surface over the ball. Do the same with corona and its an even more noticable painted on strange cross pattern.
So hopefully this gives a clear guide on why i think vray is definately better at bump and works well with hardly any tinkering. Corona as it stands is always a battle to get the bump to work and work well with the right strength. I hope its a simple fix or a scan down the chaos group code now Im guessing you have access to it - although sadly not the vrayforc4d code. Thanks again and will always chose corona over vray regardless but it would be nice to get this fixed once and for all. Cheers.
https://www.dropbox.com/s/3jofdjmnbg4rf58/corona%20bump.zip?dl=0