From what I have found, these are the available storage drivers:
Union File Systems - aufs and overlayfs
I’m currently using overlayfs and it seems to work ok but I’m not sure about it as I’ve read that it can use too many inodes which can cause problems.
Snapshot Enabled File System - btrfs
This looks like an interesting option but it isn’t recommended for production use.
Device Mapper Loopback
This uses Device Mapper over Loopback Mounted Image Files. From what I’ve read, this is a slow and unrecommend option.
Device Mapper using raw block devices
This option uses Device Mapper, usually with LVM on raw block devices. It seems to be better then the loopback option but how much I don’t know. Also on a Virtual Private Server (VPS), the raw block device is actually a virtual image file so I don’t know for sure if this helps here as the raw block device is still not really a hard disk but in a VPS, no hard disks are real so it may not matter.