The longer answer is that CC0 is not a licence – it's a public domain declaration. With CC0, you relinquish all rights to the work, including copyright. With MIT-0, you still hold the copyright; you're just allowing people to do whatever they want with the work.
Another difference is the one you alluded to. CC0 is designed for written content, images, videos, etc. It's not really designed for code/software. That's not to say you can't use it for software, however. MIT-0, on the other hand, is designed for code.
So, in essence, these two legal instruments are in a sense equivalent, but there is enough nuance there that it could make a difference in a court of law, depending on how they are interpreted.
There's also the fact that CC0 is quite a mature piece of text at this point, whereas MIT-0 is the new kid on the block. That might be something to consider, too.
Also, obligatory disclaimer that I'm not a lawyer and that this does not constitute legal advice.