I like both equally.
Chris Cornell is one of my favourite singers of all time now, but I liked RatM long before I really discovered Audioslave.
I would say both bands had very intelligent lyrics, just in different ways, which is perhaps why I couldnt choose between them. I listen to whichever I am in the mood for.
Angry usually = RatM, reflective/down/angry of a different kind = Audioslave
I just realised no one has mentioned Soundgarden yet...I actually tend to get Audioslave and Soundgarden mixed up, which is terrible, but also highlights I think that Audioslave are after a fashion a more mature Soundgarden. Even so I reckon Soundgarden were better than either band! Read the lyrics to "The Day I Tried to Live" or "Burden In My Hand" for some idea why I think so, then feel free to disagree
Dave