You can take the kid out of Yorkshire...
One thing I'm not sure Sir Patrick ever quite squared within himself. He was used to getting tapped to play kings and ministers and great heads of state, wise and weighty and all that, in his stage work. He had a bit more action in his earlier TV and film work, but Gene and Bob wanted a Captain who was more settled in himself -- mature without being old. If that makes sense. They spent time in TNG showing and telling how Picard did have his brash youth, shunning family tradition to join Starfleet, the only freshman to win the Academy marathon, the incident with the Nausicaans, taking command of the Stargazer when the Captain was killed, the Picard Maneuver, etc. But something happened in the years between losing the Stargazer and getting the Enterprise that got that out of his system. This, incidentally, is something I'm profoundly curious about, and hasn't been adequately explored in the ancillary fiction. He went from being an obscure Captain of a third-rank ship, in partial disgrace for losing said ship... to having the respect of Admirals and the clout to get the Federation's new flagship full of bleeding-edge tech. I want to see that story.
Anyway, by the time we met him, he was competent and confident and bold, without being hasty or thin-skinned (well, once we were past the growing pains of the first part of season 1). TNG showed that about the only thing that slipped through his settled rôle as master and commander of a Galaxy class starship was when history and/or archaeology was afoot, or, worse, threatened. "Time's Arrow", "Captain's Holiday", "The Chase"... But Sir Patrick chafed at always having to be the voice of reason, despite the truth of the character by that point in his life. Picard-as-action-hero started to creep in as he got more say in story. By the films, he was about to the point of full-on John McClane. Fistfights with the baddies, climbing and swinging about the set during the climactic fights, machine-guns and bared arms, getting the girl, car chases...
There are reasons I took the tone I did with him in my immediately-after-leaving-the-theater Nemesis rewrite (before I went back further and retroactively nullified the loss of the Enterprise-D and Picard-as-action-hero). I like relaxed, wry, charming Picard. That plays to a lot of Sir Patrick's strengths as a person. The best way to cap out his arc through and after TNG would be to promote him to Admiral and have him serve as a a roving ambassador-at-large for the Federation, much as Robert April had done a century earlier. We saw hints of that in TNG, in "Future Imperfect" and "All Good Things...". That is, I think, the biggest let-down for me of Picard-the-series. He should be relaxed in himself, what with no longer being in active command of a thousand-plus people, still able to get fired up about Doing The Right Thing™, but all of the unresolved-trauma-and-haunted-by-his-past stuff has no place here. It did in TNG season 4, but he moved past that. It shouldn't have been in First Contact, either. Made for good drama, but even with his often-detrimental stoicism, nine years, with Beverly and Troi there with him, should have seen him well and truly been past that.
I just recently re-read Imzadi for the umpteenth time, as well as watching "Future Imperfect", "All Good Things...", "Timeless", "Endgame", and "The Visitor" to get my fix of what FutureTrek should look like, and boy I wish this were a proper evolution of TNG: Still-active Ambassador Picard, having forestalled his Irumodic Syndrome thanks to the look forward Q afforded him; Beverly commanding the Pasteur; Admiral Riker serving out of Starbase 75 and commanding the venerable 1701-D; Wes as his first officer (and former chief engineer); Troi dividing her time between family and serving as Picard's diplomatic aide; Geordie commanding the Challenger; Worf serving as ambassador to the Klingons; Data... is a longer story. So much potential there even within the "confines" of the actual canon and the characters' authentic selves. The science-breaking Romulan supernova, the lore-breaking dystopian setting, the all-wrong æsthetic, the angst and brokenness of everyone... Pff. Toss all that crap into the nearest transporter and leave it particle-ized in deep space.