I'm about halfway through Mage, currently making my way through the rotes. It's interesting reading; the orders and paths make a lot more sense now that I know what they can actually do. The most interesting thing I've noticed is that each of the orders suggests a very different kind of camapign. It's not hard to imagine a mixed cabal, but on their own each order has its own unique set of activities.
In that sense they're much more distinct from each other than Vampire covenants. The covenants are much more different from each other politically, each having far more divergent views on the origin and purposes of their kind than the different orders do of theirs, but their core activities are all more or less similar. Each seeks to expand its own power at the expense of the others, by subverting mortal wills and weaving webs of favors and deceit. They've each got their own style, and different things they want to do with that power, but every vampire is driven by the same basic needs of territory and haven.
Mages, too, all have the same basic goal of learning secrets and advancing their power, but each of the orders has a very different set of day to day activities. The Mysterium leans towards "magical Indiana Jones," while the Guardians of the Veil are more black ops cloak and dagger. It's not simply that a guardian is "the sneaky one" and a mystagogue is "the book-ish one," filling different roles the way classes do in D&D. Each order represents its own mode of play.
The "default" mage game seems to be a mix of the different activities of the orders -- searching for mystic secrets, defending those secrets from rivals, dealing with mortals when something goes awry, and mixing it up with the local power structure. This provides another contrast with Requiem, which presents a mostly universal set of basic behaviors -- feeding, finding a haven, gaining and maintaining access to good territory -- and then layers the goals of an individual or group on top of that foundation.
Not that any given Awakened group wouldn't have its own unique features, but a game could also be defined by what it omits from the basic design. Drop the political aspect entirely, or nix adventures in long forgotten tombs. Secrecy from sleepers would be difficult to remove, being a core part of the game, but it could be de-emphasized, a barrier to other actions rather than something the group takes a proactive stance towards.
I suspect, though, that an amalgam of different styles would make for a very robust, interesting game, such that intentionally tampering with the basic mix wouldn't be worth the trouble. But a certain amount of adjustment would be inevitable; the players would naturally signal the activities they're most interested in by the order they choose for their characters, and the campaign would shift to fit those preferences. That strikes me as one of the strengths of this model -- there's a lot of variety in what a "normal" campaign might look like, and there's a built in method for the players to clearly demonstrate what they want out of the campaign.