I had no trouble seeing both Hunter's Pike and Greenwood's as the same character, or as versions of the same one. Hunter's Pike was burned out and mentally exhausted from what we can infer was a particularly rough stretch of duty, and he was experiencing pessimism and self-doubt. If the events of "The Cage" did happen also in the alternate timeline (which isn't a given), then Greenwood's Pike appears to have put it behind him and returned to what we might assume would be, for Pike, a more normal, calm and confident demeanor -- he's also had time to grow in experience and knowledge.
Your poll question, however, doesn't quite seem to be asking that.
Was Pike in ST:XI like Pike in The Cage?
* Yes, they seemed like the same character.
* Greenwood's Pike reminded me of Hunter's Pike.
* They seemed like completely different characters.
Obviously, Pike in ST:XI is not
like Pike in "The Cage" because Hunter's Pike is (by design) not himself; he's strained to the limit and on the verge of coming apart at the seams, while Greenwood's is a centered, older and wiser Pike. However, it looks like you realized that wasn't the question you really wanted to ask, and amended the thread title. Taking that as the question instead, I'd still have to go with what I said above over any of the options in the poll: I have no trouble seeing them as the same character, albeit at different points in life and under very different circumstances (and, of course, written more than forty years apart for two different mediums.)