Actually, if I'm being honest... I would have loved it if Nine could have been my Doctor, but he just wasn't around long enough. But, I love that Eccleston played a different style Doctor than we'd seen before. He still had that eccentricity, but he was a bit more contemplative, contained, and grumpy than previous versions. (And I miss, "FANTASTIC!")
That said, Tenant was around for four years which was plenty of time. Plus, he was briliant. We've seen the wacky excited Doctor before, but he still brought his own flair to it and played the part fantastically. The problem was... the writing.
When Ten was written well he was written bloody well. But the weak link was always the show runner, Russel T. Davies. It's like he didn't understand the Doctor as well as the writers that worked for him. He wrote him inconsistantly. Most of the writers on the show wrote Ten as a Doctor with one major flaw - he fell in love with everyone he met. Not just his companions, either. He fell in love with Madame De Pompadour, Joan Redfern, Wilf, The Master, Adelaide Brooke, etc... He'd say they're brilliant, get that smile on his face, and then he was gone. Suddenly he'd do ANYTHING for them - no matter the cost.
He, of course, had other layers to his character, but that was a beautiful fault that was used wonderfully for the best episodes - "Family of Blood", "Girl in the Fire Place", "Forest of the Dead". Russel T. Davies would use it too in episodes like "Waters of Mars" and even in the finale, "The End of Time", but he just handled it so... ham fistedly.
It's love - the simplest thing in the world, it doesn't need anything else. But RTD would add in every other emotion in the book. When Ten saves Adelaide Brook in "Waters of Mars" it could be this really powerful, personal moment where he can't let her die because of this flaw. Instead, he goes on this childish power trip where he gets all creepy looking and says stupid shit the Doctor never says like, "I'm the Doctor! I can do what I want!" So we spend the entire episode watching the Doctor fall for this woman and then he does it... because he has the power and that's it. Adelaide tells the Doctor no one should have that power and then goes off and shoots herself so that history doesn't change. It can end the same way without the random childishness from the Doctor. Once he saves her, instead of stomping his foot he could just immediately feel bad and apologetic. She can still storm off mad and shoot herself and then he'd feel worse.
And then there's "The End of Time". I personally thought the two parter was a mess, but there are some good moments in it. One of which is an ALMOST great scene between Tennant and Bernard Cribbins right before the Doctor saves Bernard's Wilf (cuz he loves the guy - and who wouldn't?). The two act the HELL out of the scene. But there's this one part right before Ten accepts his fate where he goes into a whiny hissy fit about how he's so awesome and could do so much more but he has to save a puny human. I understand why it's THERE but it just doesn't fit Ten AT ALL. It's like when Darth Vader has his whiny tantrum at the end of Sith. How do you make James Earl Jones sound whiny?
I think that's my biggest issue - RTD will randomly write Ten immature. There's a scene in "Voyage of the Damned" where Ten is framed by angels and he shouts, "I AM THE DOCTOR AND I AM NINE HUNDRED YEARS OLD AND I AM AWESOME SAUCE!" well, not exactly that, but basically.
He's right, he IS 900+ years old and he WOULDN'T have immature moments like that. He just WOULDN'T.
The other thing RTD liked to do is create the illusion of action. The Doctor doesn't have weopons and he can't really fight that much when he's up against aliens and creatures who could manhandle him in hand to hand combat. The good writers would do things like create tension and drama - make the Doctor be clever. RTD makes the Doctor have to be somewhere else REALLY quickly so Ten ended up running and gritting his teeth a lot in RTD episodes. Hell, half of "The End of Time Part 1" was The Doctor running after the Master. Then the Master jumped away. So the Doctor would run some more.
And RTD just wrote FAR too many episodes.
It's a shame too because the series had some amazing performances and some spectacular episodes, but so much of the writing was either just okay or just downright bad that the series never got above "Good" for me.
So as much as I loved Tennant, he just can't be my Doctor. Four's still my doctor. Then Seven. Then Five.