I would recommend checking out the multiplayer then. The campaign has the problem that armies will rarely be evenly matched, but in MP both sides get about the same amount of resources for building their troops. There's also the scenario battles.
The campaign is definitely about getting a doomstack (or 5) and going to town. If by the end of the campaign you aren't rolling through everything, you're either on Legendary or you've made a mistake. Greenskins, especially, are like this. You end up with 10+ armies, all of them carefully moving around in encamp stance so that you don't lose your WAAAGHs. On the other hand, the greenskin early game is a massive party of slaughter and conquest.
If you want factions that play very differently from the two you've tried already, the Undead, WElves, and Beasts are all much more unique. Beasts, especially, since they are about ambushing, picking fights, running away, and combat management.