When the departure of David Tennant was announced, the backlash was imminent. Various protests of "But they can't change the Doctor!" were thrown around, despite the fact that this had happened nine times already. The BBC, apparently anticipating the backlash, took a year off and did a year of "David Tennant specials" to keep the momentum up but still allow for cooldown time.
But it didn't completely work. There are indeed some who consider Doctor Who to have ended with Tennant's departure. I have heard people criticize this point of view, saying things like "These people don't like Doctor Who, they just like David Tennant."
While it's unfair to judge an entire group of people like this, I nevertheless feel that it may be an accurate description of at least some of these people.
Anyone who says that Doctor Who was ruined after David Tennant left, but never actually watched the show after David Tennant left has little argument to stand on. I'm not saying that everybody has to love the 11th Doctor; I keep trying to stress that everyone is allowed to have their own opinions.
However, I will stand by my argument that if you haven't actually watched the post-Tennant show, you probably are ill-equipped to form an objective opinion. It's like trying a new food; you don't really know if you don't like it if you never try it. You can say "I won't like it" all you want, but you might be saying that about a future favorite food.
The 5th Doctor himself once said it best regarding regenerations, "You never know what you're going to get." Indeed, I personally know many, many people who were avid David Tennant fans dreading the change who have now fallen in love with Matt Smith as the 11th Doctor.
The overall success of the change is in no small part due to the other drastic change, the replacement of showrunner Russell T. Davies with Steven Moffat, who wrote many fan-favorite episodes such as "The Empty Child/The Doctor Dances," "Blink," and "Silence in the Library/Forest of the Dead." Moffatt's dark but playful sense of storytelling worked well with this new Doctor to put a new spin on the show. He worked to make sure that 11's run wasn't a pale imitation of 10's, but its own entity entirely.
In that way, it's actually a bit unfair to compare any of the Doctors' runs to each other. Each one was different. 1 was a sci-fi hodge-podge, 2 was more focused 60's sci-fi, 3 was a sci-spy show, 4 was comedy mixed with gothic horror, 5 was a little bit of everything, 6 alternated between grim and goofy, 7 was sci-fi as told by the Brothers Grimm, 8... never got a chance to have a "type," 9 was edgy, 10 was a romp through time and space, and 11 is science fantasy.
To be completely honest, these may all just as well be different shows. So, to all you fans of the Doctor out there, keep this in mind.
Don't think of it as the Doctor's run ending, think of it as a brand new show beginning.
The Doctor shows his companions, us included, the wonders of the universe. In return for that, he gets the loyalty of his companions, no matter which face he wears. Sarah-Jane stayed by 4, Peri stayed by 6, Rose stayed by 10. Shouldn't we at least give each new Doctor the courtesy of giving him a chance?
...that goes for Peter Capaldi, as well, Smith fans.