I keep the smaller dies in the plastic bags they came in and hang them from a pegboard. I only have one of the longer strip dies and that one gets stored flat on the table beside my Sizzix Bigshot Pro, with nothing else on it. I also have one of the go cubes which is its own storage container.
i read something where someone had kept their long strip dies stored leaning against a wall and it got warped. I think they had it standing on end, but even so I would be worried about storing a long one in the sorter if it wasn't supported on both ends. The sorters look to me like they're designed to hold the regular sized go dies rather than the long ones.
i think the problem with storing them flat occurs if they are stacked.
Rob