for me, its mainly temperament.
If its a horse with a nice temperament but only a little training, I don't care I can train it so long as its got a good willing-to-learn temperament. But if its the grouchiest thing you ever saw then it doesn't matter how much training its had.... its just never going to be the horse for me,
When I bestride him, I soar, I am a hawk: he trots the air; the earth sings when he touches it; the basest horn of his hoof is more musical than the pipe of Hermes. ~William Shakespeare