To add to other people's anecdotal evidence, Trello is painfully slow for the board I use the most. Perhaps I over-use it - I have 27 lists, the longest of which has some 1500 cards. But it's slow to the point where Chrome asks if I want to kill the tab at least once every 2 days.

It works fine for other boards, so I assume it wasn't built with so many lists+cards in mind. But the fact it, it can be slow, almost unusable, at least for certain use cases.