Our memories of TOS are weird. Red Letter Media in one of their recent episodes made a good point that many of the qualities we ascribe to him - Shatners. Broken. Delivery, or Kirk kissing all the girls - aren't as present on watching the series, but seem to have been formed from parodies or one off iconic events. I think Shatner, the man, also gets confused with Kirk, and some of the former's personality flaws.
Kirk was far less of a jerk than people make out he was.
He didn't have the patrician liberal / aesthetic sensibilities of Picard, but he was a humanist, not the meat head jock of Kurzman Trek. The key to TOS was the comradeship between Spock, Bones and Kirk. Onscreen, at least, Kirk "wins" hands down for his warmth. Movie Kirk or TMP or WOK are the ones that I most like as a person.
Its intriguing the way the captains, kind of encapsulate elements of their times. Kirk is a rugged wild-west individualist. Picard is the face of the nineties rules-based world order - you can imagine him at the UN eloquently arguing a human rights case. Sisko introduces Clintonian / Bush era cynicism. Janeway was initially a harder Picard, but she became warmer as the series progressed.