Either one is fine, but "for the inconvenience" is more common and is easier to say (it has one less syllable!). As for who is accountable - it depends on the context and the culture. If I was late and kept someone waiting, I would definitely say "sorry for the inconvenience" and I think it should be clear that I am taking responsibility for this inconvenience. But if my brother is late and has not arrived yet, I might also say "sorry for the inconvenience" even though it is clearly my brother that is causing the inconvenience. Some people (and cultures) are quick to apologize and others see it as a sign of weakness, so there are no firm rules. But generally people should apologize when they have caused a problem or an inconvenience. And you can apologize for something that isn't your fault - it will generally be appreciated and understood that you are just acknowledging their is a problem, even if you aren't the cause. I hope that helps.

For the inconvenience.