The audience for a thriller generally seems much more skewed towards an older audience with many of the characters being in their twenties onwards, the characters themselves often going through some very adult trauma, for example shutter island, the main characters wife drowned their three children and he killed her but felt to blame so he retreated into psychological delusions, where he is the hero.
They often let the audience put together what they think happened throughout the film, or to interpret the ending how they see fit.
Most often they feature twist endings, built to shock the viewer allow repeat viewings of the film to better understand its meaning or what it is trying to put across to the audience. Quite often these 'twists' feature extensive foreshadowing throughout the film, requiring the audience to pay attention to not just the character but the things happening around them to ensure maximum understanding of the events that take place throughout the film.
Often films in the genre are limited on budget for example Donnie Darko, and yet other films such as Shutter island and Vanilla sky have much larger budgets and yet Vanilla sky as a film didn't preform as well as Shutter Island in the box office, despite having several big name stars involved. Most films in the genre tend to show patterns of being received better by the public than by critics. This could be because of fans of the genre being more interested in the genre as a whole than the critics, however some films are ( add films+ IMDB info) positively received by critics and yet preform poorly in the box office and don't really become all too popular until the have finished their initial box office run, for example Fight club.
The BBFC rating for psychological thriller tend to follow the trend that the viewers are more mature, with very few being under the 15 certificate.