We use both. Oyster shell stays in the gut for a longer time and some of it may not be absorbed if the system is fast. (All the grit I find in my water trough's "poo sludge" leads me to believe some of the shell isn't being absorbed.) I think the whole egg shell actually gets absorbed versus oyster shell.
No matter what the source, not all will go straight to shells, it all goes through the system, so you don't get a 1 for 1 ratio on shells. Your blood needs calcium for proper blood cell growth.
I feed them raw. I just through the egg shells into a 1 gallon ice cream bucket and about once a week I change it out. About a week later I crush them and send it out to the girls. I guess it depends on how much air you let them breathe and if you have a dry-ish house. I'm in Oregon so I know it's pretty moist air most of the year. But we don't have a smell problem as long as there's no broken yolk or anything like that.