I suspect Karen's question isn't the screw-top vial vs. shell vial debate, but what containers to store them in once you already have gone with shell vials. There are of course lots of pro's and con's to each setup, although heat-sealing cotton plugged shell vials is not one of them - it's just as fast as packaging individual screw tops, you just end up spilling a little bit of ethanol.
Here at the Cal Academy our entire collection is housed in standard height shell vials with screw top jars. The jars are standardized and uniform, making them fit snugly in our metal rack system. They are also less bulky than the parfait style bail-tops so you can house more vials per jar, more jars on a shelf, and handle the jar racks more comfortably. The white lids also make writing or labeling the tops quick and easy. We do store multiple genera per jar and divide up the space with plastic dividers/liners for maximal space efficiency. Of course if the jar's aren't sufficiently tightened there is significant risk of evaporation, within a year it's usually easy to pick out a jar from a lineup that wasn't fully tightened.
I've worked with collections that are bail-topped and they are cumbersome. The latex/rubber liners need to be replaced more frequently than a screw top lid, and the price of the bail jars is *significantly* higher. But there is only one way to close the jar so there aren't any left accidentally loose. Not sure which is best, I think cost drove a lot of the decisions to go with screw top here and I don't think we're any worse off for having gone that direction.