Despite physical paper today is believed to be deprecated, I think that’s not entirely true! In multiple meeting circumstances, looking at a computer to discuss past or feature tasks, is just not convenient, specially for quick short note taking. It is much easier and faster to draft sketches and notes by hand in paper than typing it.
As such, one huge feature that is missing in Trello too (at least out of the box), is the ability to export a board or a folder to a PDF or a print view that is suitable for printing. Obviously, a simple print from the browser would grasp the job, however, when you have tons of tasks and people, it become unfeasible. Moreover, the customization of the layout for printing is also an important part of this feature.
Generally, I would take this feature as one of the main flags that would favor Infinity over Trello.