Then, somewhat more recently (for me, a noob to her journal) dawn_felagund wrote on a similar topic: plot arising from character, and conversely, characters arising from plot. As she notes, the word "story" is usually defined as a sequence of events, while things like character motivation are extra, and therefore absent from the basic definition.
I'm going to hit on the plot-wrter vs. character-writer bit first, because theme is a different beast.
When I read the first post, my first thought was, "I'm both, it just depends on the context." As I've tried to get away from fanfic the last six months or so, I've noticed huge differences in how I approach my original work compared to fan work. When I'm approaching a fanfic, I primarily take the tack of, "What would happen if X and Y were locked in a prison cell together?" and run with that inspiration. Sometimes I start with plot ("How would Tellius end up in a world war and awaken the goddess if the Serenes Massacre never happened?" - which is not the plot of the Chronicle, but could be), but most of the time I'm interested in character interaction.
With no established characters ready, I can't do this with original fiction. With no fully established setting to work with, in addition, I can't even start with more than a bare-bones plot. "An elderly naturalist is pulled out of retirement to study flora on an alien world." It has potential. There's a character - sort of - and a setting-- sort of. But I came up with this to fit the requirements of a call for anthology submissions, so the character isn't even really my idea. They asked for older protagonists, and the setting has to be fantasy or SF; I could've gone anywhere with those guidelines, but the story prompt above (because that's what it is, a prodding to go further and come up with real ideas) is not very creative. They might get five stories with the same premise.
I didn't have much to go on until I considered what kind of story I wanted. You might say I started thinking about theme: is this going to reflect environmental concerns? Should I try to address the issue of colonization, how it can destroy ecosystems? Or will this be a story about age discrimination, or about trying and failing to enact change? Consider writing a fanfic AU for a minute - when you throw a character you know into a different setting or situation, part of the interest (for me, anyway) is to see how they react to different decisions, or explore what changes will happen if you throw them into an environment that would shape them differently. In the same way, it seems to be that this elderly female naturalist will become a different character depending on which situation I throw her into, so at some point - usually the beginning - I need this basic idea, this theme, to direct my characterization and setting details, even if the story ends up changing and suggesting a different one later.
Digression: I see a huge appeal in creating a world and set of characters, and then writing a million books about them - even if the stories end up repeating themselves eventually. That would be a huge advantage when sitting down to do the actual writing. I wouldn't run into the above problem at all. That, I feel, would be the sure way to maintaining one's income. And if the series becomes self-referential and starts fan-pandering, well, you do want to maintain your fanbase, don't you?
Anyway, as I kept thinking about the question of what drives a story, and how that affects its appeal, I came to the conclusion that for me, in my jumbled-up opinion, it all eventually comes out to the same thing. You may be a character writer, but characters create plot-- they have to, in most cases, or people lose interest. If your character sits and stares out a window and does nothing, and doesn't think about much, nobody gives a damn. If she does something-- plot. Instantly. Bam. She does something, and there's going to be motivation in there somewhere, which is created by history, which in turn creates the present situation, and plot. I was told over and over that conflict makes plot, but I think it's more accurate to say character makes plot, and most characters, like most people, are going to be conflicted about something. People create conflict, and the rest is just nature.
Likewise, plot can't happen without a character. You can take a plot-based approach, but it seems to me that in the course of writing your story, you'll take that character you created to fill a role and make him evolve almost by accident. In my experience, one can create a thoroughly thought-out character, fill in all the blanks on the personality and history sheet, and still not know anything about them until you start writing, at which point they take on a life of their own. You never (well, I never) end up with the same character you started out with. And presumably, as you write and get to know these people, you will care about them at least as much as the plot.
So I guess to me, the idea of being a plot or character writer doesn't make sense, because to me they are exactly the same thing. My bare-bones plot up there suggests a character by default. If you cut it in half and pretend that "to study flora on an alien world" was the only idea I had, well, I need someone to enact the plot. No getting around it. But even if I have a whole plot mapped out, and start with that driving my process, the character will eventually become the most important part of the story, and therefore be the driving force. I think this is a matter of layers - the first draft, or first layer, is driven by one thing; the next one might end up driven by something else. But the finished product will probably be moved by each in equal measure.
That's all idealism up there. And I can't lie and say I've never come across a plot writer, because Arthur C. Clarke is one such, and Tolkien didn't spend too much time on individual characterization as I recall. It's there, but clearly is not the focus, especially in something like The Silmarillion. I may love Maglor, but if I'm going to write a story about him, I have to make shit up right and left. All Tolkien gave me were events and some indicators of feeling. If I work only with that, I'll write a cliche.
I'd say more about theme, which was the whole point of writing this entry, but that'll take another six or seven paragraphs, and this is already too long.
EDIT: there's discussion in the comments on DW if you're interested in that.