It is difficult to break down the huge Comparison of Whonix and Tails to primary differences.
Anyway, I'd say:
- Tails: concentrates on being a Live DVD / Live USB; being amnesic; mobile market
- Whonix: concentrates on "keep user safe, even when running arbitrary, leaky non-Tor-safe applications and servers through Tor"; support customization to your heart's content (as in tunnel VPN/proxy/i2p/JonDo etc. through Tor); location hidden servers; installed on computer
I am a maintainer of Whonix.
I have been researching this field for a media project I am working on, and while I am in no way qualified to answer this question as well as others here, it seems to me that Whonix is the thing to use if you are using your personal home computer, for the best possible safety and anonymity. While Tails is probably best used for short periods of time on a dedicated secondary mobile platform that is not used for anything personal - ever. Whonix is not safe for local forensics while Tails is. ;)
Whonix consists of two virtual machines, a gateway and a workstation. The Whonix-Gateway can be installed in a virtual machine to route all traffic through tor from any other virtual machine. The second virtual machine can be any OS. It doesn't necessarily have to be the Whonix-Workstation. In virtualbox, under the network settings for the second virtual machine, select 'Internal Network' from the 'Attached to' drop-down box and set 'Whonix' as the name.
TailsOS (The Amnesic Incongito Live System)
TailsOS boots off USB and puts you in a live Debian-based linux instance configured to give you out-of-the-box anonymity on potentially any computer system (home, public computer, library, etc.). It spoofs MAC address, uses Tor to hide IP, and includes a browser and application suite chosen (and in some cases specially modified) to enhance privacy. The other prominent feature of the system is that it is designed to leave no trace of your activity, so if your USB stick ever gets lost or compromised, there is no personal information and nothing that can be gleaned about your specific usage. Tails does optionally allow you to keep some information persistent if you enable the persistent volume option. If this is enabled the little information that is persistent (PGP keys, Bitcoin wallet info, wifi passwords, etc.) are all stored in a secure encrypted persistent volume.
dead simple to use
boots off USB and works on any machine (even older machines)
leaves no trace of activity (in logs, page files, bash history, browsing history, anything!)
pretty idiot proof (by design)
downside of lack of persistence is that you're tied to the software versions in your tails install, if the Tor browser gets updated or a critical OS vulnerability gets patched you can't just do an apt-get update (technically you can, but it'll revert to the old version every time you boot), so you might be left vulnerable until the next TailsOS version is released
browser plugin choices are limited by the desire to make sure the browser fingerprint isn't too unique (which might identify TailsOS users), so the Tails browser plugin suite will seem quite lacking to advanced users
Like TailsOS, Whonix protects anonymity by using the Tor system to hide your IP while you are in a protected Debian-based linux instance. Unlike Tails, Whonix runs in a virtual machine (actually two virtual machines). One VM runs the actual OS and browser (the Workstation) and the other VM is responsible for running Tor and acts as a gateway to the Internet (the Gateway). The fact that the Workstation is isolated from the internet and can only access the internet through the Gateway means that it is nearly impossible for your IP to leak (because the Workstation doesn't even know what your IP is). The other big difference between Whonix and Tails is that Whonix is not meant to be "amnesic", so the system will retain all your forensic history unless you take steps to securely wipe it.
Isolation of Workstation from network is a huge advantage for keeping your IP address private--even if your browser (or any other application in the Workstation) is fully compromised, it's impossible for it to reveal your IP because it doesn't know your IP!
Persistence means you can run whatever you want in the workstation and update programs as soon as the updates become available
Complicated to setup and requires administrator/root privileges
High system requirements (need modern hardware that supports visualization technologies, lots of RAM, etc)
Persistence means that if your system is ever compromised, stored personal information and your browsing activity could be discovered