In terms of slaan gimmicks/specialities/their unique stuffs:
Mazdamundi's encourages and rewards infrastructure-heavy play because the geomantic web basically gets stronger the more territory you have and the more developed that territory is, encouraging both tall and wide building basically. He benefits off of that a bunch.
Chaacalot is basically your intrigue guy - his magic speciality is illusions and mind control, his mist unique thing is something he can eventually cast to do bullshit like hide whole fleets of ships he's in from detection or possibly whole planets later on in the game once you have the Web up to a level that can support something like that.
Adohi-Tegha (who I'd have named Talezkop if he didn't have a canon name) is basically your DPS slaan. He does 'I throw asteroids' level telekinesis on the regular (once you get to space at least), summons firestorms, zaps everything with lightning, caster-type shit. He can also pull a pseudo-Eldar by looking into the future or looking through the warp for specific shit, which is useful if you can figure out the missing context.
Zaqunda is the tank. He can block shit like nobody's business, eventually get to rezzing relic priests a lot earlier than the others, and also do some other stuff relating to ressurection and healing and shielding and shit. You get the idea.
Huintenuchli is basically a steady boost to tech growth through the whole game, good at inventing new shit to deal with unexpected situations, and can do cool technomancy shit like take control of enemy guns so they stop working and only shoot when pointed at their own side.
Kroak is a bit lopsided in comparison - he's a boost to early game and late game, with a bit of a lack in the middle, since he remembers a bunch of Old Ones shit that gives you a boost in the beginning tech and faction-wise, but nothing much for the middle game. Late game is when you're able to ressurect him, which has obvious benefits, and he'd also be the one to consult when trying to make new slaan (which is possible for everyone, he just makes it slightly easier).
Hopefully that clears up stuff for anyone who was confused. I sleep now.