This is an interesting discussion, and while I'd like to point out that a great story had better have both great characters and great plot, there is a definite difference between the two in storytelling.
Let me explain. First, let's get the basics out of the way and describe what makes a story plot-based, and what makes one character-based. The essential difference is seen when we look at what drives the story along. In one that is plot-based, the plot itself is what drives the story to conclusion. Point A naturally leads to Point B, which then uncovers Point C, which leads us to the eventual Point D. Things that happen along the way are what point the tale in the next direction.
But how is that different than any story, you might ask? That's what plot does, after all. Yes, that is what plot does, but it's not always what drives the story. In a character-based story, it's the characters' decisions, based on who they are as a person that drive the plot. It's their interaction with each other that makes the plot come together, not just what they must accomplish along the way.
Well, that's fine, you say, but characters interact with each other. It's kind of their job as characters. Again, yes. But in this case, they're what pushes the plot along, not the other way around. Let's look at a couple of examples.
The first story we'll look at is J.R.R. Tolkien's Lord of the Rings. While each character is unique, and brings a different perspective to the story, the story itself is plot-based. There is a goal to achieve, and it really doesn't matter who is achieving it, the desired end result is the same. Certain requisite tasks must be completed to satisfy the plot. Sure, certain characters must do specific tasks, but it's still very task-based, not something that happens as a result of specific character interaction. Frodo Baggins must return the ring to Mordor, and that is because of his unique character. The thing is, anyone possessing that specific character trait would have made a fantastic substitute and the plot would have remained the same.
Now let's look at Alexander Nabokov's Lolita, a very character-based story. The entire plot is driven by the interaction between Humbert Humbert and Dolores Haze. Sure, there was an end goal in Humbert's mind, but it was specifically the interaction between him and his Lolita that caused the tale to go as it did. Substitute a different Humbert and the story would have been much, much different. Substitute a different Lolita, and she would also not have reacted the same way Dolores Haze did when confronted with any of the situations she was. And each of the characters in the novel brought a different twist of the plot into the story with the way they reacted to what was going on. The entire story revolves around how they react to each other's desires and motives with their own.
There is a theme here. Many stories of action, suspense, and horror genres are plot-based, while many dramas are character-based. But that's not to say there's a line drawn in the sand firmly separating each into respective sides. An action piece can easily be a character-driven story. I'm writing one right now, and it's firmly in the character-based camp.
Sometimes it isn't really all that obvious which a story is until you think about it. They do overlap. The way a character acts often drives the plot as much as anything, and many times things outside the realm of a character's motives influence the plot. It really didn't dawn on me my latest sci-fi time travel romp was character-based until well into the story. You might not tend to think of science fiction action stories as being all that character-based, after all.
The television series Firefly was, though. That story was all about how the characters interacted among themselves, and you know if you were to have substituted any other character for one of them, things would have gone quite differently along the way. It's the epitome of a character-based story. And when you compare it to Star Wars, for example, the differences between what drives the action in both stories are obvious. "Defeat the Empire by becoming a Jedi Knight, destroying the Death Star, and confronting Darth Vader" sounds far different than "Our previous contact had some serious issues with how we handled the last job, and that is having a direct impact on our current job".
Now that's not to say that characters are simply interchangeable in a plot-based tale either. Hardly so. The Indiana Jones movies are all very much plot-based, and I dare you to replace that iconic figure with anyone different and have it turn out nearly as well. One could argue that same point with a number of great characters in plot-based stories. They're great characters for a reason. They just don't drive the story, the plot does.
If it isn't terribly obvious which side a story falls on, take a look at what causes the conflict or action. Many times a plot-based story relies on a plot device to cause the action. Two characters are fighting over the same thing. Two characters want different results for the same quandary. Compare that to a plot that hinges more on the action and reaction of the characters based on who they are as characters rather than simply their goals. Another way to think of this discussion is in terms of a story being motive-based rather than goal-based.
So what's the best type of story, plot- or character-based? Of course that's completely unanswerable. At least I think so. They're both great in their own way. I like characters with a little more meat on their bones. That is to say well rounded, and less cardboard-y. That doesn't mean that plot-based stories lend themselves to cardboard characters, and it doesn't mean a good plot that really pulls the story along isn't necessary for character-driven stories either. Both are essential elements of storytelling.
My bottom line is I use whatever moves the story in the right direction. If it's the necessity of getting from Point A to eventual Point D, then I roll with it. If it's letting the plot flow based on the interactions of the characters, their motives and decisions, then that works too.
Go with what works for your story. If you figure out which type yours most closely follows, you might have an easier time figuring out what to do if the story stalls, but in the end, it really doesn't matter much. As long as something pulls the plot along and makes it go somewhere.