I've seen a LOT of people very conflicted about Ten, which interests me from the fannish perspective, cos I think a lot of the fans who are very focused in a one OR the other sort of way re Eccleston and Tennant and Ninth Doctor and Tenth Doctor are folks who were, with the new series, new Whovians. This is their first regeneration.
And intellectually knowing that they have been other Doctors prior to the Ninth, and there will be other Doctors after him, is one thing. But in their hearts the Doctor is Eccleston and no-one else. And you can argue logic with people cos it involves their brains. But one can never argue feelings cos hearts don't operate that way. (trust me--I just had a 15 minute convo with my Judy about this, wherein she was very skeptical about this whole Ten thing)
Okay, so here's my thing:
I think the human heart has an infinite capacity for love.
No-one expects you to make a choice. No-one is holding a gun to your heard, saying you HAVE to chose one or the other. There is no choice to be made--the realities of casting have made a choice for us (that there will be no more Ninth Doctor television adventures) and that can be hard to accept. But loving the Tenth Doctor (or even just liking him) changes one's love of the Ninth Doctor not one wit.
It's perfectly fine to love the Doctor in more than one incarnation. It's never a betrayal of either one Doctor over another, or fans of one over the other. It's all a big love-fest. And you'll make new memories from watching the Tenth Doctor, that will never replace the memories you have of the Ninth Doctor's episodes and your fannish experiences with friends re: the 1st series.
No-one is saying you HAVE to love one incarnation of Doctor more than another, and no-one has the right to judge you by which Doctor you love the very most, or the reasons why. If you like Nine best? That's just fine, so long as you do not insist everyone else follow your example. You adore Ten? Shiny! But you're not allowed to make a Nine-only fan feel bad for not loving Ten as well. And it's perfectly fine and natural to love them both, too. In the end, whether it's Nine or Ten or Five or Three or Eight or even ONE, they're all the Doctor, and we love the Doctor. Period. Full stop.
The thing of it is, a character is MORE than just the actor who portrays him. A character is a group effort. Television, unlike novels, is a collaborative medium. Characters are the result of the writer's words, brought to life by the actor, shepherded by the director, and nurtured by the other cast members and characters.
We the fans may have lost Chris Eccleston as the Doctor, but that doesn't mean that we've lost everything we loved. Nor does it mean we may never get it back. It'll be different, yeah. But it always is. That family that brought us the character we love is still there. We trusted them to give us stories we love once; why should we stop trusting? Part of the love of fiction is allowing it to affect us--bring us joy AND pain. The way I see it, everybody's doing their job, and that just makes me excited. Because I get MORE STORIES YAY!
And it doesn't matter that they won't be exactly the same stories. Heck, every new Who episode changed the characters and premise a bit, until the people we said good-bye for a while to in POTW were very different from the people we'd met in "Rose." That's PART of falling in love with an on-going series, yeah?
So relax, and keep an open mind, and don't worry. It's all good.