Does similar writing style tell us the writers are similar with respect to some measure/perspective?
To me the most obvious similarity factor would be culture/schooling. And that also creates a large confounder for the things you ask about (personality etc.) 

A bit of searching did find a paper from 1981 by Ruffner &amp; Burgoon, but it has very few citations. It also uses a pretty antiquated personality test (the Omnibus Personality Inventory). The climax of the paper is predicting various stylistic aspects using personality and education aspects: