1 - FAF is more symmetrical. The factions are barely different, compared to the three races in SC1/SC2.
2 - FAF is designed to be playable with lower APM. You can do more to automate your armies, like setting factories to "infinite build" and it is more viable to queue up lots of orders (telling your engineer to build 20 buildings is normal in FAF, I think that's less normal in SC2 and of course impossible in Brood War)
3 - The primary game-ending mechanics are different. In both games, "send a big army to your opponent's base/expansion and wreck it" can be a viable strategy. But in FAF you can also kill the enemy ACU to win. There is nothing like that in StarCraft, where you have to kill every building to win. Also, in StarCraft, people can "mine out" resources and that is often a way that the game ends (and the fear of mining out forces people to attack). In FAF, mexes never run out, but the game becomes more dangerous as time goes on. Nukes, heavy artillery, and experimentals ultimately can break basically any base/expansion. In the early game and mid-game, you can take and hold mexes in the middle of the map. As the game goes on, it is normal for there to be a "no man's land" between the two (or more) bases where nothing can survive.
4 - There is less quirkiness. In StarCraft, upgrades are important, but there is nothing really equivalent to upgrades in FAF. Also, in StarCraft, spells are very important. There's basically only one "spell" in SupCom, overcharge, which is VERY important. But it is just the one.
In StarCraft, units do different "types" of damage so some units are better at hurting other units, e.g. vultures are great against drones but not against Ultralisk, because they are coded to do "concussive" damage. FAF does not have that, a point of damage is a point. Of course in FAF There are some units that are better at killing other types of units, but it's more obvious what is going on. You can see it more easily with your eyes. You don't need to consult a chart to know which units are effective against other units. You can see whether units are dodging shots, whether splash damage is hurting lots of units, etc. Even though FAF has more units than SC2, it's actually less complicated because the units fit neatly into certain categories, both because of the symmetry between factions, and just because there are fewer types of attacks in FAF. Every unit does not have its own quirky identity, in FAF, nearly AS MUCH as in StarCraft games.
5 - you don't have to be deliberate about expanding. In StarCraft, taking an expansion is expensive and you need to think carefully before you expand. But in FAF, it can be as simple as dropping an engineer out of a transport and building 4 mexes (4 mexes cost 132 mass, which is like 2.5 tanks, it's incredibly cheap, and it pays for itself in less than 30 seconds). Of course it costs more mass to lock down the expansions with factories, turrets, etc. But the point is: you generally want to grab as much as you can as fast as you can.
6 - FAF deals with scale much better. In StarCraft, battlecruisers are the size of about 10 marines. In FAF, there is much more diversity/disparity in unit size. This is one of the neatest things about FAF. You can zoom out and you should probably zoom and play zoomed out so you can see what's going on.
7 - You can scale up economy without expanding. In StarCraft, if you sit on one base, you WILL fall behind in economy compared to someone who takes 4 bases, and you will eventually "mine out." In SupCom, you can upgrade mexes to grow your economy. Expanding and grabbing lots of T1 mexes is usually more efficient than upgrading mexes to T2 right away, so you want to expand at the start of the match. But eventually it can be good to upgrade mexes (depending on the map/situation) and I don't think there's anything comparable in StarCraft. Yes, you can boost economy by making more workers, but it's just not the same, because you become saturated and eventually you mine out. It's a mistake to start upgrading mexes too early, or to upgrade mexes that can easily be killed, but at some point it can become necessary to upgrade mexes, and there's just nothing comparable in StarCraft.
8 - Unit cap tends to be less important. A major part of StarCraft is the 200 "supply cap." Bigger units use more cap. You have to play around the cap, making enough supply depots etc. and when you get maxed out, you need to attack your opponent or else you just stop making units, or you need to sacrifice some vultures/SCVs so you can make more siege tanks. In FAF, a mech marine takes as much cap as a Megalith. While there is still a unit cap, it was meant to avoid the game taking up too much memory. It wasn't meant to be an important gameplay mechanic that determines when people attack vs. defend. You still need to pay attention to the cap, but it's pretty easy to play around it in FAF, compared to in Brood War/SC2. There is basically no such thing as a "maxed out army" in FAF.
9 - reclaim. It's extremely important as a gameplay mechanic and there's just nothing like it in StarCraft.