I'd like to believe that Quote or Curly alone wouldn't have triumphed over Ballos. Without the both of them, to watch each other's back, it would have ended differently. Work together, live together or fall alone.
As for Miakid vs the Doctor...
We don't know much except, it appears victory against him was unclear. He looks tougher than the Doctor, and if he had a role in the invasion or War, then perhaps similar to his appearence, he looks much tougher than the Doctor. And if he was possibly military, or had an army...
On the other hand the Doctor only was able to assemble a ragtag frenzied Mimiga bunch, while Miakid may have led a War with superior resources...
The major trump card the Doctor has though, would be his Red Crystal. Cheating death might give him victory, after all, how do you fight the red mist?
Still, I'll place my bet on Miakid. Fighting experience should not be underestimated.
No comment on the "all mimigas ever", we know little to nothing about them outside the events occuring during Cave Story.