Wianno,
In terms of how big a factor is (percentage of links with) nofollow, the thing you need to understand is a site with zero nofollow links or a very low percentage comparatively will look somewhat unnatural. As to precisely what that percentage needs to be, no one knows. For you, with 54%, that is really high (probably looks pretty natural though) and it prevents you from getting the link juice from all those sites. So, assuming you and your competitor have a similar number of total links, they will rank higher because they are getting juice from nearly twice as many links as you. Most of our client sites range from 1% to 10% of links as no follow.
The major factor in MozTrust is having "trusted sites" link to you or be linked to someone linking to you:
"MozTrust can be improved by getting links from other sites with high MozTrust such as goverment institutions and universities."
The description of looking at it like six degrees of separation says it best to me, if FDA.gov links to site A, and site A links to site B, and site B links to your site then that is likely providing a bit of a boost in mozTrust. (Obvious is FDA.gov linking to your site would be best.) If a site 4 degrees removed had an FDA.gov link, it would have less value to you than the first example. Then, the more trusted sites that are close in degrees of separation to you, the more mozTrust you shall be afforded.
As to high no follow and trust there is no correlation based on the definition of mozTrust: "...MozRank measures the link juice (ranking power) of both internal and external links..."
MozTrust is based on a seed group of trusted sites like government and educational sites. It is based on the number of these links and how often you get them: "Receiving links from sources which have inherent trust, such as the homepages of major university websites or certain governmental web pages, is a strong trust endorsement. By measuring the occurrence and frequency of these endorsements, MozTrust can quantify trust on the web."
So, from this I ascertain that if you had ten no follow links over 4 to 6 months from various government, .edu, and say wikipedia sites and half of them were no followed, it would still have a value that was based on getting a lot in a short amount of time. So if my competitor got the five links that were followed but not the 5 no follows, I would have more mozTrust.
Hope I did not confuse, In case I did, here is where it all comes from in the land of moz..... (What the heck is MozTrust?) (What is MozRank?)
Best