The results are different if you save the curve that you worked with Rhino 6 as an illustrator file.
Is there a solution?
Ensure your model isn’t too far from world origin (nor too huge).
The same result occurs when the curve is close to the origin.
Couple of other things to try -
- Run SimplifyCrv on the curves
- Explode the polycurves into single elements (lines, arcs, etc.)
Thanks Helvetosaur! 
I solved it with Explodes, but it seems to be a lot of trouble.
Can you post the Rhino file here (just the sample you showed above)?
Curve Test.3dm (1011.9 KB)
The curves look very clean in rhino and it seems to open OK in Illustrator CC here…
(this is saving from Rhino V6 as .ai)
Thank you for your test.
You may want to experiment with the Preserve model scale setting in the AI export.
-Pascal