Good question. I haven't read any research on the topic but my years of UX testing and experience have taught me that it depends on the site, the site's design,the content structure and the end user profile.
The IA of the site is the 1st determining factor and design is the 2nd. Assuming that you have the first one done perfectly for your target user, design errors or weaknesses can undermine your main or side navigation.
I just finished a UX test series where we thought we had it all right but there was a disconnect between the design of the main navigation and what was happening on the page. It was super simple main nav with wonderful side nav support... The main nav just didn't work. We tweaked the labels, retested, and then made some major changes to the main nav/page design in order to augment the connection between the two and then finally had the desired result.
I don't think there is a one or the other answer... navigation needs to work with ALL elements of each page.