Not to get into another canon argument with you (please!), but this is like the situation with Zephram Cochrane... two different actors playing the characters decades apart, with completely different interpretations that completely screw up the timeline.
If Pike was morose and brooding in "The Cage" - just think how much MORE upset he'd be if he had to contend with an arrogant little smartass like Kirk at the same time!
Well, I've said before that the two versions of Cochrane don't screw up anything; after all, his two appearances were 205 years apart. I'm not the same person now that I was 20 years ago; just imagine how unrecognizable a man's personality could be after more than 200 years. The only problem I have with First Contact
is that James Cromwell was way too old for the role, given the chronology "Metamorphosis" established.
And I don't think your assessment of Pike makes any sense at all. Remember, the Pike in "The Cage" wasn't just "upset" or "brooding" -- he was grieving after the death of several of his crew.
Combine that with the fatigue the entire crew was showing at the start of "The Cage," and it's understandable that Pike could've been suffering from an uncharacteristic state of depression.
So prior to 2009, we never actually saw what Christopher Pike's normal
personality was like, except maybe for that last minute or two of "The Cage" after he beamed back up from Talos IV and seemed a lot more cheerful. So there's no reason at all why Greenwood's Pike couldn't be representative of what the man was normally like when he wasn't depressed and in mourning. We simply don't know enough about Pike's normal personality to rule that out. And since it's the only other canonical example of the character that we have, there's no valid reason not to accept it.