Whonix can be configured to be not persistent, and Tails can be configured to be persistent. Out of the box configuration is the biggest difference. However, Whonix is set up to be run as a set of virtual machines. One of the reasons I like Whonix better is that this dual virtual machine setup means that, should you get kicked off of Tor in the virtual machine that acts as a gateway, the other virtual machine does not have any fallback connection, effectively preventing accidental access of the internet while unprotected.
The added risk to Whonix is that if your host system is sufficiently compromised, there's no real guarantee of anonymity. A lot of people end up running Tails in a VM, though, and someone has to be pretty serious about wanting to see what you're doing for that to be a real issue.
It can mount HD, but the read/write privileges are the same as any other OS I imagine. I've copied files from my HD to Tails, but I've yet to try dropping files into the shared folder on my HD.
The biggest difference is that Tails is designed to be entirely amnesiac, and leave no forensic trace. Whonix is a persistent system.