Originally Posted by The Glyphstone
They're compatible enough that you could take spirits from one and drop them in the other without issue. You really need Book of Spirits to flesh them out for either venue, though.
They're pretty fleshed out for Werewolf, getting probably a good fifth of the core book with lots of time in most of the Werewolf supplements. In Mage, you get 2 or so pages about the spirits in core, which necessarily leaves a pretty basic picture and basically need to look elsewhere to really understand them.
Systemically they're identical, although the Mage core just lays out the barebones of their mechanical capabilities.