I'd also argue, Christopher, that while 10 and 11 do share characteristics, I'd hardly call 9 and 10 similar.
As I've been saying all along, it's not all-or-nothing. I have so much trouble communicating online, because I always think in nuances and matters of degree while the Internet is dominated by arguments cast in terms of opposing absolutes, so people keep assuming I'm making black-or-white cases and it's so frustrating saying no, no, I'm talking about varying shades of gray. I'm not saying there's no difference
at all between Eccleston and Tennant; I'm saying their differences are proportionately less than the typical difference between consecutive Doctors in the classic series. If nothing else, they
look more similar to each other than any two consecutive classic Doctors. There wasn't a great difference in age or body type, and their wardrobe, while distinct, was less flamboyant than the looks of classic Doctors, so the differences were subtler.
Back in high school and college, I had a friend who was into a bunch of SF and comics but hadn't seen
Doctor Who, so he only really knew about it from what I told him about it (the same way I only really knew Marvel Comics from what he told me). One day, we were in a bookstore together and came across
this edition of The Doctor Who Programme Guide, and it was the first time he'd seen the faces of the different Doctors. He'd known that several different actors had played the Doctor, but he was surprised that they looked so different from each other. He'd just assumed they'd all be generally in a similar range of age and appearance, like the different actors to play James Bond or Superman. I think that if he'd seen pictures of Eccleston, Tennant, and Smith side by side instead, he wouldn't have been so surprised that they played the same character. Obviously they did have differences, but not as massively as their predecessors.
Yes, they had angst and all, but then again, Ten was visibly more jubilant and willing to be the hero than Nine, who was just trying to be one. Nine's resentment over the humans had died out as Ten, and again, he was a more joyful, enthusiastic kinda guy. Nine was too, but he was more at-home with the tough choices than Ten was. So I'd say Nine's progression in series 1 lent the seeds to Ten.
Of course, but that's a difference of degree, a shift of emphasis. You have to look closely and get to know the characters to see it. Superficially, Eccleston had a lot of goofiness and enthusiasm and humor. And Tennant had plenty of angst and inner turmoil. It was more a difference of proportion than anything else. I think that gets exaggerated in our memories because that's how memory works -- we keep track of people based on how they differ from each other, so those differences are amplified in our memories. (It's been shown that people recognize cartoon caricatures of real people more easily than photographs, because caricatures reflect how our brains model information about faces, weighting their distinctive features more heavily than their more ordinary features.)