Do people get less airsick if cabin pressure is at 6000 ft.?
Boeing supported a study that directly addresses your question:


  On the basis of our findings, we conclude that maintaining a cabin altitude of 6000 ft or lower on long-duration commercial flights will reduce the occurrence of discomfort among passengers.


Note, though, that the lower cabin altitude of the 787 is one of its selling points, and the study was conducted not too long before that type's introduction. However, its methods seem reasonable (at least to someone like me with no background in health sciences) and it was published in an important peer-reviewed medical journal.

The Aerospace Medical Association took a broad look at existing literature on the subject shortly after Boeing's study. That review


  did not find sufficient scientific data to recommend a change in the cabin altitude of transport category aircraft;


however, the authors did not dismiss the notion that a lower altitude may increase comfort, and they recommended further study. Just this month, some results of that further study were released. The results showed


  no adverse effects from an environment pressurized to the equivalent of 8000 ft compared to 6000 ft,


although they did not account rigorously for the subjective "discomfort" that I think you mean by "airsick."

My reading of the current research (based on the above) is that there is no evidence to suggest that a 6000-foot cabin altitude is medically better than a higher altitude (up to 8000 feet), but it might make some folks subjectively feel better.