Great points have been made here.

I, too, think the answer is both.

If a sub is known for taking a greater amount of pain in subspace, than the dom/me needs to be aware of this.

If there a limits like allergies or physical ailments, partners need to be aware of this also.

For example, someone with bad circulation doesn't need the tightest bondage available.

Someone recovering from an injury doesn't need to be flogged in that spot.

And for those "pain sluts" who don't know when to say no - I once met a man who enjoyed pain so much, he told me, "You could cut my arm off and I wouldn't care when I'm in subspace", - let's have those in the top role take some extra precautions and be aware of what they are doing.

Before, during and after play, how much responsiblity may be shifted with the power exchange, but I believe the total responsiblity is with both players to make a session/scene and its aftermath a success.