Ok, I'll try it, alhough all the information is based on 3.81
Ered Luin:
Ered Luin focuses on heavy infantry and strong heroes. They excel in their defensive capabilities but lack in speed. Their heroes are famous for being overpowered (due to runes or just the amount of heroes, or maybe its just Thorin) and can easily turn the fight. As stated in the "Path to Edain 4.0" threads they still will have many heroes but in an altered way (expect a lot of hero summonings).
So Ered Luin is good if you like slow but strong infantry and heroes.
Iron Hills:
The Iron Hills feature the fastest dwarven units and are, in my opinin, the strongest of the three factions in 3.81. While fast and strong in the offensive they are somewhat less tanky than their brothers from the other realms (although still tankier than petty humans
). Their archers are counted among the best, Iron Hill archers with fire arrows were a dangerous foe. Their heroes are more or less supports, focusing on the early and midgame, losing in the lategame. But if used wisely Dain, Thorin , Murin and Drar are also able to turn the tide of battle.
Iron Hills are therfore a good choice if you want to end the game fast and if you like to harass the enemy with the unexpected speed (again, Iron Hill Dwarves are also able to win a fight against most other units, they even win quicker than the other realms, they just take more damage).
Erebor:
Erebor is a faction that focuses on anti- structure units. They arent as tanky or as fast as the dwarves from the other realms and their axe throwers lack in range, but instead they can destroy structures as easily as heavy armored opponents.
In my opinion Erebor excels in the late game when you have upgrades at hand, especially because the axe throwers do not need fire arrows but are fine with forged blades (upgraded axe throwers are beasts ^^).
Their hero league is more or less well rounded, they have anti- structure heroes, Gimli, and one of the strongest late- game supports in the game, Dain (Thorin is also a good choice, but who wouldnt buy Gimli instead?).
So, you should pick Erebor if you face an army of heavy armored units or if you expect the game to take really long. One can always count on an army of upgraded Erebor Dwarves if its not against the elves