Button opens 50%. We 3bet from BB 12%.

Flop comes Q T 8 with (lets say) 2 hearts.
Do we have range advantage? Should we do betting on flop?

First I thought 3bettor has the range advantage, but I'm not sure.
My thinking is that he BTN might have more J9 combos and sets meaning BTN has more "nutted" range, but 3bettor has more stronger draws.

How should we approach the spot with our range? Do we cbet more or check more?
Do we have C/R range? What is it?

Thanks for input. Spot is really tough to me and I kind a don't know how to deal with it.

In the hand I got T998ds hand with only backdoor flush draw.. How to play this hand?:)