This can't be answered accurately without a description of the villain. You need to have an idea of his range so you can tell whether or not a shove gets you more value. It would be extremely helpful if we had an idea of whether or not he would raise with a flush draw on the flop, or if we had an idea as to what type of hands he min-raises on a turn like this. With how this played out and no idea how the villain plays I would lean towards flat calling. I'd do this because I think that if the villain has any clue what he is doing at all he will realize that a min-r on that turn is still going to allow you to draw with spades, so the flush seems a bit more likely than the straight. He could easily have a hand like Ks3x or just not be a thinking player though.