I would disagree that Tarkin shows any anger in ANH. Unlike Vader, who is pretty much calm throughout OT, Tarkin does raise his vice here and there. However, I would not call it anger. He seems to be on top of things all the time. He does seem to be annoyed sometimes though, e.g. “she lied to us!”.
Yes, I agree, it’s more annoyment than anger; however, I find a big difference between the range of emotions his human self expresses in ANH and what they have him be in RO.
What I was trying to emphasize is that this being a problem that has to do with the way the lines sound/are delivered as well, it can’t be charged on the CGI but on the very way the character is written, or acted, or directed.
EDIT: There is only one moment I remember from RO when he does something more natural, which is a gesture with his face while saying “rebellion” (if I remember right), a sort of “that will do” assertion.
It is difficult to compare to Cushing’s acting. However, I found the whole thing good enough and I am quite happy with it. I think the film would be weaker without Tarkin.