Okay, I have played quite a few battles now over the last year. 95% of these have been solo fights. One thing has become clear to me. The following dwarf list can stand up to just about anything (note that I have not fought it against barbarians, yet).

King x1, Crossbows x2, Ranger x1, Mighty Cannon x1, Warriors x4

They have plenty of firepower to thin on coming enemies. And lots of Fighting to deal with what gets close. The orcs due to their cheap nature can sometimes give a good show against them with their great number of units, but their about it. Undead and Sorcerer Legion need to wait till their forces arrive to begin an assault and during this time they can suffer massive losses, sometimes even costing the game before it even really gets going. Elves can line up and fire back, but if they miss and fail to take out the dwarf shooters, their low fighting make them easy targets for the return fire.

That's not to say that my dwarves don't lose, just not very often. Maybe something like 85% wins.