Awfull print

On the left a small part printed on Prusa i3; ABS 0.2mm layers.
On the right, same part printed in Lulzbot TAZ4 with Slic3r ABS profiles, medium quality. PET surface.
The ABS are different colors but same brand.

What may be the cause of such a horrible print ?

Another picture showing the print from the side will be telling.

Here it is. FYI, it is 20mm wide.

Can you post one showing just the side? You may have z-axis artifacts/banding:

Orias, i dont understand you when you say the side. It is such simple part that i have shown photos of every part of if!

I think he is looking for something from the edge-on as opposed to from above at an angle. Seeing that can differentiate between different types of banding and help narrow down the cause. Check your hobbed bolt for plastic in the teeth. Sometimes if there is one or two adjacent teeth with plastic in them, and the hobb makes one revolution every two or three layers it can look like screw-related banding when it’s really extruder-related. Are the bands are the same spacing as the screw threads?

Yes, the wobble is about the same distance as the Z screw threads. But is not simetrical in both sides. In one side of the cilinder the bands are higher than the oposite side.
Something like this:

Side A:…Side B: