In no particular order, here are several candidates:
Current version at faforever.com (the main page, scroll down to see it)
Chunky mechs and tanks, jets and all the other classic war toys. For those that love vanilla-warfare.
Stealthy and fast spiderbots, walking ships and pointy structures. You like being the edgy guy with spikes.
Floating alien tanks, shields on everything and space donuts. You want to sweat microing your units.
Chicken ACU, chicken assault bots and chicken experimental. You want a balanced army of chickens.
The United Earth Federation is a powerful human faction aiming to unify a splintered empire through conventional weapons. They pack a powerful punch when it comes to damaging structures with their artillery, supported by satellites. Or defending outposts with their unique Tier 3 rotating Gatling gun as point defense.
Cybran units are often insect-like in appearance. They use laser, stealth and cloaking technology more than any other faction. Their stealth bombers are powerful and if their naval has killed everything on sea, some ships can simply walk on land to carry out even more destruction.
Humans who follow the philosophy of the aliens. Their experimental unit Paragon can generate nearly limitless resources, but if it explodes it causes a nuclear strike. They use hover technology and can nullify shields or use guided missiles which are fragile, but do very high damage on impact.
Religious aliens who came with superior technologies to cleanse the galaxy. They have multipurpose units, the strongest shields and a gigantic experimental Bomber. The experimental building Yolona Oss creates the most damaging and devastating strategic missiles ever seen.
UEF - Unite the galaxy using overwhelming force and powerful defences
Cybran - Liberate the galaxy with ambushes and trickery
Aeon - Cleanse the galaxy with highly specialised units each excelling at a particular role
Seraphim - Annihilate the galaxy with smaller numbers of advanced technological units
From me @arma473
Order: The United Earth Federation is the successor to the empire that once controlled the galaxy. The UEF imposes its authority with durable armies designed to control territory.
Freedom: The Cybran Nation began as a cyborg conspiracy to liberate workers enslaved by the Earth Empire. Because it began as a resistance movement using hit-and-run tactics, its armies are fast, stealthy, and versatile.
Purity: The Aeon Illuminate is a religious order based on devotion and sacrifice. Followers of "The Way" are zealous and single-minded missionaries. Aeon units tend to excel at only one single purpose.
Revenge: The Seraphim are alien invaders from another dimension. Seeking revenge for a bio-weapon attack by the Earth Empire, and fearing humanity's genocidal intentions, Seraphim weapons create overwhelming destruction.