It's funny because both moves require opposite DI. First I'll talk about D-throw.
Generally there are 2 ways to DI Brawler's D-throw and that is either away or directly above him. Against Piston Punch you'd want to DI away to avoid being combo'd, since the move is a vertical hitting attack, this makes it harder for him as well as reducing the vertical distance. For Helicopter Kick, you want to DI behind so that you're directly above him, this makes it harder for him to connect his Helicopter Kick and it reduces the horizontal distance.
When it comes to stage positioning, you're generally safe against Piston Punch if you stay near the bottom and next to the ledge. This of course, is the exact place you DON'T want to be against Helicopter Kick, against that move you'd want to be in the very middle, which is where Piston Punch wants you and on top of platforms of course.
Now, for the actual DIng. I've concluded that holding directly towards the stage help you live a tiny bit longer against Helicopter Kick, no holding up or down. Against Piston Punch, you'd want to again, do the exact opposite. Hold down and away from the stage.
Both moves are generally similar, but Helicopter Kick has the advantage mostly due to the fact that you can get yourself and the opponent in a combo closer to the horizontal blast zones than you can with the vertical blast zone. An opponent who knows better about Piston Punch will avoid platforms at all costs and stay as low as to the ground as they can. Against Helicopter Kick... its harder to avoid being near the ledge because that's generally where you go when you lose stage control. In a nutshell, HK rewards for taking stage control where as PP makes you give your opponent stage control, and even then hey could time you out if they wanted to by camping near the edges of the stage sitting in shield. Because lets be honest, what are you going to do to them?
Should also mention that PP has to fight against many things such as stages without platforms and fall speeds making vertical killing harder. When HK does its business it doesn't matter how heavy you are if it can bring you all the way out to the blast zone before sending you off. Feint Jump also compliments HK more because of how the kick sends the opponent horizontally into a combo.