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Tails and Whonix both can run in VirtualBox. Tails doesn't recommends it for security reasons (https://tails.boum.org/doc/advanced_topics/virtualization/index.en.html), for Whonix it seems to be a standard mode of operation.
What are the design differences which makes Whonix more secure to use it together with VirtualBox in comparison to Tails?
See also:
Different threat models.
Whonix (needs to) assumes, that the host is safe. (Tails needs to assume this as well to some degree, because I suppose, many users are downloading and burning/installing Tails using their host, where malware could interfere.)
Tails is more focusing on being amnesic. Whonix is more concerned about misbehaving applications and leaks. Therefore Whonix is not amnesic. While there is no substitute for Whonix's lack of an amnesic feature, full disk encryption is recommended. Each project made a trade-off. (It would be nice to combine both, but we're not there development wise.)
Full disclosure:
I am a maintainer of Whonix.
