Flat matchbooks make a lot more sense...easier to store & look at, take up less room, not such a fire hazard. That said, if I wanted to be sensible, I probably wouldn't collect matchbooks anyway! (not to mention ashtrays, chips, soaps, sugars, swizzle sticks... )

My husband and I both prefer full books...as a collectible, the covers are more interesting than the matches (other than feature matches, of course), but there would have been no reason to make the covers if it weren't for the matches. So, we prefer to have full matchbooks. However, IF we have duplicates or triplicates I will usually remove the matches from one book and put that cover in a binder.

For full (or partial) books, we have a few sets of storage drawers. The matches go into small ziplock bags, which are tagged with the casino name, and filed alphabetically. Almost all of them are stored open, so they can be looked at without opening and closing the book which would weaken the hinge.

For older or rarer books, only 1-2 matchbooks per bag...facing opposite directions, to distribute the bulk

For newer & more common books, I put several in the same bag

One drawer holds matchbooks that are too long or too wide to fit the drawers comfortably, match boxes and feature matchbooks. At one time I played with the thought of putting covers into sportscard protectors...bad idea (cost & space), but the ones I encased are in that drawer.

This probably isn't the best way to store them, but it's worked for us so far.