I don't think you can say Morrison tried to be Mick...Too utterly different guys and mindsets. Morrison viewed music as something more than just music. The guy was a poet first, rockstar second, crooner third. Mick was a rockstar first, entertainer second, lyricist third. While I love the Stones, I do think Morrison had more artistic integrity. I know he ensured that while he was alive none of The Doors music was used for commercials, even though the other 3 guys wanted to do it. The guy viewed music as art...I don't know what Mick views music as.
The thing is, I think The Doors meant every little way they experimented. Like, it wasn't just a joke to them. Whereas with the Stones, at least Mick looks at albums like Their Satanic Majesties' and songs like Lady Jane as sort of jokes...Doesn't really value them for what they are and keeps to the Stones image. The Doors, Morrison at least, tried to be different than that. He grew his beard out specifically to test people: To see if he was loved just for being "Jim Morrison of The Doors", or if he was loved for just being a person. A guy who broke boundaries and didn't care about taboos and had a good time doing so.
Mick may have rolled his eyes while changing the lyrics of Let's Spend the Night Together on Ed Sullivan...But Jim just sang the actual lyric in Light My Fire because he didn't give a damn about censorship.
I always thought of Mick as sort of a poseur. He sings about drugs and all this stuff, but I don't think he actually lived it as much as his songs would make you think. Keith did, Keith's never been a pretender--He's a true no BS rocker. I'm not saying that diminishes Mick as an entertainer; He's an amazing singer, dancer and lyricist...But he didn't really live the life he sang about; Morrison did and sadly paid the price for it.
I mean consider 1967:

1970:

While Morrison didn't destroy his mind or his talent like poor Brian did...He did destroy his body and like Brian became a casualty of the 60s/70s. I respect guys like Brian, Keith, and Morrison more than I respect Mick because they lived (and in some cases, died) the life they sang about. Keith and Brian were the real deal and Brian and Morrison were like the Princes of the Psychedelic era.