Well I'd take issue with the use of the word 'power'. What is meant by that: hard power? Soft power? What do you mean?
My opinion is that they don't, however that's based mainly on hard power (because I'm a realist). In terms of soft power they are the main actors, while in terms of hard power that remains in the hands of states.
Hard power matters more to me; I view it as more significant and that is why I believe corporations do not have as much or more power than governments.