I'm not sure what exactly you mean by a dominant draw; do you mean that you are an equity favorite over villain's range? Or that you are an equity favorite over the drawing hands in his range?

Anyway, for me position and stack sizes are among the leading factors in determining whether to push or pull with a draw. If you're in position with a big draw then still you may opt to flat call if you're fairly certain that villain has a set, right? And if you have a weakish draw but your opponent seems timid then you may choose to play it fast hoping he'll lay down part of his range; also, you sometimes play dominated draws fast to get it HU (cleaning up outs), etc.