Hi Remo,
The artefacts that you are seeing are not caused by the resolution of the image but by the bit depth. An 8-bit image used as displacement will always create that stair-step effect.
I've attached an image with two screenshots: one example of an 8-bit and highly compressed texture used as displacement and another where I've taken the same texture, change it to 32bits in Photoshop and applied an gaussian blur with a radius of 3. It's obvious that the details will be blurred but you will smooth out the steps.
I hope this helps,
Bogdan
Cinema4D R17 / Windows 7 on Intel i7-3930K / 32 GB Ram / GTX 670 / GTX 780 / 3 x GTX 970 on Amfeltech expansion cluster