Would Pussygate have been more damaging against another candidate?

[Sumner 1868]

Yes, but mostly because of how they probably would have responded. Drumpf used a combination of whataboutism and defense of his comments as harmless "locker room" banter. Essentially, he managed to have it both ways; his whataboutism abut Bill Clinton kept Republican-leaning women on his side, while his defense of his comments in the face of calls to drop out energized male conservatives.

Now let's say that Kasich had been the GOP candidate caught on tape. He probably would have said something like "I didn't actually say that, but I'm really sorry anyway." This hurts him because he fails to benefit either way; his apology upsets conservatives who like that kind of rhetoric, while his denial is attacked for being an obviously lie. After a couple days of media attacks for lying, Kasich changes his story and acknowledges the recording is true while condemning his comments. So now Kasich is a hypocrite, liar, and a self-admitted sexual harasser. He loses easily.