Terrasaur player here! Gonna try a synopsis of faction playstyles; here we go!
The Shadowsun Syndicate: Ultraman Business Ninjas. All about speed, stealth, and then hitting that fucker hard, as far as I can tell. Mini-ninjas and jets are tough, and the cars can drag around shadow gates, giving you more stealth and teleports [including Skyscrapers, be sure to grab some!]. Not to great at control, though.
The Martian Menace: Various martian invader archetypes. All flying, all shooting. They love farming power dice, having vanguards harass for more dice, hunters pick off important units, and saucers/power pods supporting/controlling. Be sure to grab a TV network for propaganda! Not sure on the weakness, flying can be tough to deal with, but I guess choosing between defense and offense, as well as keeping your saucers and pods safe.
Planet Eaters: Heard alot about them in this thread, alot of expendable, but powerful, units, and a big focus on the monster, who will often easily gain tons of power dice simply through attrition, and power up his units.