This guide is for both CoH veterans and new players.
It has been only couple days since the game came out, thus some information this guide has may change in the near future.
You can use Ctrl+F feature to go to a certain content you're interested in.
(Ex: Searching '2. US Force')

1. Summary for each factions
2. US Forces (USF)
3. UK Forces (UKF)
4. Wehrmacht (WM)
5. Deutsches Afrika Korps (DAK)
6. My personal opinions for each factions

Keep in mind that I'm not a native english speaker.
Some words used might be not fully describe what I really meant, and names of abilities/units might be off.

US Forces (USF): Aggressive faction. It has a good early game with strong infantries combined with light vehicles, and can either keep winning or turning a game around with various upgrades. Compare to other factions, USF offers various strategical choices for multiple playstyles. However, new players might feel bit overwhelmed.

UK Forces (UKF): Balanced faction. Infantry, mech, artillery, call-in units, everything is decent on this faction. It's main weakness is that it's not particularly strong at anything, but it's a well-balanced faction that is for both experienced players and new players.

Wehrmacht (WM): Defensive faction. It's like the opposite of USF. Its units aren't really mobile, but they're good at forming a frontline and pushing slowly. Its main game play goal is embracing and fortifying, and eventually build a strong army with leveld-up infantries and powerful tanks.

Deutsche Afrika Korps (DAK): Mobile faction. It has various light vehicles that are strong when used right, and they even enhance its infantry units. DAK might be not the best at face-to-face massive battle, but its ability to control multiple parts of a map and also flanking enemy forces with the mobility is their main strength. However, it is not recommended for new players.

What determines the overall game plan for USF is 'Suppert Centers'.
There are three types of support centers.

- Air Support Center
Offers recon, bombing, suppressing fire from aircrafts.
- Mechanized Support Center
Enhances tanks with various abilities.
- Infantry Support Center
Gives infantries upgrades such as additional health, grenades, anti-tank mines.

Each battlegroups have ways to compliment the support center choices.

- Airborne Battlegroup
The recon from the air support center can provide a sight for the paratroopers or the supply drop.
The paratroopers can be enhanced with the infantry support center.
- Armored Battlegroup
The mechanized support center can enhance call-in tanks that are already powerful.
- Special Operations Battlegroup
It offers a light vehicle, the commando squad, smoke screen, AT gun, MLRS, infantry buff.
It works the best with the infantry support center.

USF has good base units as well-
The riflemen squad is the main infantry of USF. (It gets even more powerful with M1918 Browning auto rifle upgrade.)
1/4-ton 4x4 Truck and M8 Greyhound can harass opponents with good mobility.
M3 Amored Personnel Carrier can be converted into 3 different types: Anti-infantry, anti-vehicle, medic.
For anti-tank, there are the Bazooka squad and M24 Chaffee light tank.
M18 Hellcat tank destroyer really do destroy tanks, and it's GOOD at it.
M4A1 Sherman is a versatile medium tank.
And there are also the mortar/Machinegun team and a sniper.

It might not have as many options as USF has, but it has efficient upgrades and stable unit combinations.
The infantry section can specd into sniping, anti-tank, or anti-infantry.
There are vehicles that can support them usch as Dingo light scout car, Humber armored car, M3 Stuart light tank.
UKF also has many choices for tanks for each situations.

While each individual units aren't game-changing by themselves, UKF has one of the best battlegroups.

- Indian Artillery Battlegroup
Offers a powerful artillery and infantry buff. The artillery feels stronger than that on the previous CoH games.
Gurkha rifles section is surely one of the best infantry units in the entire game.
- British Amored Battlegroup
Reduces the cost for the royal engineer section, and allows to build a repair center.
Also, offers 3 different call-in tanks, air strike and air recon.
- British Air and Sea Battlegroup
The commando squad has a grenade, sticky bomb, explosives bag, and it becomes undetectable while in cover.
The incendiary strike helps a lot when pushing a frontline.
Has various defensive options such as sector artillery, naval guns, and an ability to block neutral capture points from opponents.

WM is strong at turtling when winning, or slowly building up an army to strike back with when losing.
The last tier building offers StoBtruppen squad, which is an insanely powerful infantry, and super-strong tanks.
For the base infantry, there are the grenadier squad for the versatility, Jager squad for the medium-ranged combat and Panzer grenadier squad.
Wm is a defensive faction, thus defensive units such as the machine gun team, mortar team and sniper can all be produced from the tier 1 building.

Grenadier squad and other infantry squads can be used during early to mid game, until WM gets the powerful tanks
Or, tier 3 and 4 unites can be untilized such as Flak 30 AA gun, Pak 40 AT gun, Stug lll G Assault gun.
No matter what path was chosen, the main game plan for WM is minimizing early unit losses, and building up an army for the late game.

- Mechanized Battlegroup
Offers upgrades for veihcles and for StoBtruppen squad
Can be versatile with artillery, 4 diefferent tanks.
- Breakthrough Battlegroup
Specialized in offense.
The faction is still fundamentally defensive, but this battlegroup makes it stronger when WM has to push in.
Offers options for both viehcles and infantries, along with other aggressive options such as smoke screen and incendiary strike.
- Luftwaffe Battlegroup
Various air craft supports like air strike and air borne.
Can get AA tank without getting on Tier 3.
Offers strong AT options with AT gun call-in and AT gun structure.

If you're still learning WM, I recommend Luftwaffe Battlegroup, because its tools fit to the fundamental of the faction the most.

DAK has good units, but they all require a good micro control.
It's a vehicle focused faction. Even infantries like Panzergrenadiers or Assault Grenadiers get a buff when they're near a viehlce.
It also has many call-in units.
Marder lll H tank destroyer from tier 3 is a strong anti-tank unit that can be used until the late game.
254 Reconnaissance Tractor offers HE/Smoke strike and also an ability to detect enemy units.
It has the strongest tank in the game, Tiger tank.
Armory offers various upgrades.

Tier 2 and 3 can be upgraded.
Upgrade tier 2 to get Flakvierling Half-track and le.IG 18 Support gun team for anti-infantry.
Upgrade tier 3 to get Stug lll Assault gun for the firepower and 18-tonne Recovery Half-track for the utility.

- Italian Infantry Battlegroup
Offers Guastatori squad, a light vehicle, artillery, booby trap, and other various skills.
It's versatile, and Guastatori is busted with the flamethrower.
- Italian Combined Arms Battlegroup
Bersalieri is an extremely mobile infantry that helps to control a map.
Also offers decent vehicles, air strike and artillery.
- Armored Support Battlegroup
Enhances tanks a lot with multiple abilities.
Has air support such as air strike, and utilities like an ability to get resource from a destroyed tank.

There's no 'right' choice or a playstyle for this faction, so it's important to find what works for you.

It has only been couple days since the release, so nobody can really be sure about anything yet.
However, it's still clear that DAK has couple infantries that are way too strong. Bersalieri on 1v1, and Guastatori with the flamethrower on any maps and game modes.

USF seems the weakest faction for now, because the defensive options of WM are too strong, and DAK has good anti-infantry capability.

UKF used to always have a weakness no matter what playstyle you choose on the previous games, but on CoH 3, it's well-balanced and stable. But it still struggles because of the lack of a finishing move.

After the nerf of DAK, my personal tier list looks like this:
WM > UKF > DAK > USF