I'm not sure if this is the fault of David Tennant or the writers during his tenure, but I grew tired of Tennant once I realized one thing:
He played an interstellar time-traveling Steve Irwin with a deus ex machina grossly misnamed a "sonic screwdriver" that was able to do ANYTHING except apparently screw or unscrew things.
"Hey look, it's certain death! IMMA GO POKE IT WITH A STICK!" is how I would describe Tennant's portrayal of the Doctor in most dangerous situations. Which is not to say that he didn't do a good job, or that it was even his fault...it just got old.
I preferred Eccleston's "You would not BELIEVE the s*&^ I've been through" portrayal of the Doctor as a darker character haunted by the nightmare he survived and the terrible choices he was forced to make by his own people.
I would certainly hope that if they had it to do over again, they would do a much better job of it.
I never was that big a fan of Billie Piper's character, and could not understand the foaming-at-the-mouth fanatics demanding she return. She didn't have much purpose in life, no dreams goals or aspirations, and the Doctor didn't even change her to give her any outside of being with him. Such an empty shell of a character.
I like Matt Smith's portrayal as the guy who does NOT know f*&^all about every bloody thing, and finds much more joy in new experiences. I also enjoy his quirky mannerisms and the fact that the character doesn't take himself seriously or act serious unless he absolutely has to. Given that past doctors quite frankly abandoned their companions on alien planets in alien times, often without their consent, I value the current Doctor's loyalty to his friends. I think Tennant's goodbye scene at his end was part of that connection where he realized their importance in his life, both old (Lethbridge-stewart and Sarah Jane) and new (sarah jane's adopted son and Rose and others) and decided he was not willing to lose anyone else again. That was why when (spoiler removed) happened to (spoiler removed), he took it quite badly. He'd decided that would never happen again, gave it EVERYTHING he could to prevent it, and was unable in the end to stop it.
Anyway, kind of a tangent there. Basically, watch it whenever, don't take it too seriously, and just enjoy whatever parts of it strike your fancy. Everyone's different so everyone has parts they like or dislike. For an example, I thought Midnight was boring, and the only important part of the whole episode in relation to the overall story was when the professor's assistant mentioned they were doing research on the lost moon of Poosh.
But whatever you enjoy, you're entitled to and I refuse to call anyone out on their opinion, because that's what it is. If a particular Doctor/Actor/writer/companion/story touched you in a particular way due to your personality or things in your life that made it click particularly with you, who am I to judge?