Please note that Herm has left a lot of things hazy, whether because those bits haven't been developed yet or because de wants to design things to balance threat levels nicely with other worlds.
Top powers at beginning of worldgate events: Soprone, unnamed fragmented empire, unnamed sea power, unnamed rocca land/continent. The first three of these are sea powers; the last is not, but consists of an entire continent overrun by highly efficient, hugely strong nomadic horse archers, and so deserves listing.
The larger 'horses' are horses as we'd know them, except bigger - to carry a rocca and accoutrements without difficulty. Tall faleighs can be better off with one of these.
Cavalry lancers ?? - still in use in bloodsports involving riding around and stabbing things.
The precise amount of punch a military mage corps can pack is still undecided, primarily because I want to get a good balance of power between worlds.
Battle mage units are always trained together. Strong camaraderie is especially important because of the somewhat chaotic nature of Muttiverse magic and the ways in which it's controlled -- you need to anticipate what your teammates are thinking.
Counter-magic is obviously important.
Chaotic methods and tactics are used to good effect by Iceheart's troops, who want the enemy never to know whether they're about to throw big rocks or set things on fire or alter the terrain, etc. They are highly organised; they just look unpredictable.
Shade's great strength, and where I think it outclasses both Eodea and Steamy, is in 'intelligent' magic (no, not MI yet) or magic used for calculations. This includes magical crypto, highly complex spells and spells that can run somewhat on their own and react to changed circumstances.
Comms magic is going to be key as soon as someone works out a reliable method that doesn't require line-of-sight.