I dunno, I feel like murder might be a teensy bit worse.
Maybe.
I'm going to have to tread lightly here, but consider this:
A murder ends the life of a person. It affects them (obviously) and the people who know and love them. That said, it affects a fairly targeted, relatively small group of people.
A false rape accusation, on the other hand, affects the accused as well as affecting a much larger number of people.
If it's never exposed as a lie, the accused is sent to prison, their reputation is ruined, and it affects the people who know and love them in that they either now consider this person as a rapist, or they view them as incorrectly accused and their faith in the social fabric and justice system is shaken or destroyed.
If it is exposed as a lie, the accused may walk free but their reputation has still been dragged through the mud, and some may be suspicious of their true innocence. Meanwhile, it affects large swaths of men and women who now are more defensive and suspicious with regard to rape charges, and furthermore it affects men and women who have been raped because they're less likely to want to come forward in an environment of such suspicion. If the person went to jail before the lie was exposed, a false rape accusation can shake large groups of people's faith in the justice system and law enforcement as a whole.
I'm not attempting to downplay murder here, but I think there's an argument to be made that a false rape accusation IS in fact one of the worst things you can possibly do. I think it is, along with false accusations of any serious crime.
As a side note: this does not mean I think that if a person is acquitted of rape that the accuser should be faced with the harshest penalties we have. The burden of guilt is just as high going the other way, if you ask me -- you'd have to prove beyond a reasonable doubt that the accusation was done with intent to harm or for personal gain, not as a mistake or simply not having enough evidence to find the other person guilty.