This proves that it's just a bit weird to rank modern stories in the same list as classic stories. I know it's the same show, but in many ways it's also very, very different. Hell, even comparing Hartnell to Pertwee, or Baker, or McCoy is difficult for that reason.
I don't agree with a lot of the choices here, but eh, you always get that with lists like this. I definitely would put Eleventh Hour above Rose or Christmas Invasion - neither episode is really good. You could argue that Rose was an important landmark for the show, but that doesn't make it good - and that would mean Unearthly Child should be way higher as well (although the last three episodes kinda ruin it, the first episode is still damn good). Eleventh Hour and most of season 5 (and some parts of season 6) actually was very heavy on the Douglas Addams influences, which is what makes me love those seasons.
I'm bad with choosing favorites, but even though Androzani is good, I wouldn't rate it quite so high. That story felt more like a high point in a period where the show was already starting to lose itself (and went completely off the rails after that). There have been better stories before. I would choose City of Death as my favorite, but that may be clouded in nostalgia as that was my first story, which I saw in one of the happiest periods of my life and which started my sick obsession with this show.
We made some lists in one of the recent Doctor Who threads of our personal favorite stories for each Doctor (which I think is a bit more useful in ranking these stories), and I still stand by my list:
Hartnell: The Time Meddler (or: First episode of Unearthly Child, Marco Polo, Aztecs, Gunfighters, War Machines)
Throughton: The War Games (or: Power of the Daleks, Faceless Ones, Evil of the Daleks, Tomb of the Cybermen, Abominable Snowmen, Enemy of the World, Seeds of Death)
Pertwee: The Green Death (or: Terror of the Autons, Mind of Evil, Daemons, Time Monster (it's crap but super enjoyable crap), Three Doctors, Invasion of the Dinosaurs (see Time Monster)
Tom Baker: City of Death (or: Ark in Space, Genesis of the Daleks, Brain of Morbius, Seeds of Doom, Masque of Mandragora, Robots of Death, Deadly Assassin, Talons of Weng-Chian, Horror of Fang Rock, Shada)
Davison: Caves of Androzani (not a fan of the last part of the classic series, so no runner ups I'm afraid. Not familiar enough with the stories either)
Colin Baker: The Two Doctors
McCoy: Ghost Light
McGann: Night of the Doctor (the movie was crap, so not much choice here)
Hurt: Day of the Doctor (again, not much choice here. Although I liked the episode with his earlier cameo a lot as well, but that was more a Smith episode)
Eccleston: The Empty Child/The Doctor Dances
Tennant: Girl in the Fireplace
Smith: Vincent and the Doctor
Capaldi (so far, early days): Listen
Of those Doctors/stories, my favorites would have to be Hartnell, Throughton (I have a major soft spot for 60s scifi, but I understand it's not for everyone), Tom Baker, and Smith. Really happy with Capaldi as well, he could join my list of favorites, but we'll have to see more of him first. Season 5 is the high point of the modern series, season 13 and 14 the high point of the classic series (Tom Baker's second and third series). Vincent and the Doctor is easily the high point of the modern series. No other episode has come close. I hope we'll ever get an episode that comes close to that again.
Best Doctor: always Throughton.
Everything in this post is the truth.