Let's back up for a moment because on the surface both of those methods sound virtually identical. The difference is that character development assumes that the character will, fundamentally, change over the course of storytelling. Character arcs, on the other hand, assume that the character remains largely static, accumulating experiences and new ideas but not changing on a fundamental level. The easy shorthand is to ask whether or not the character would make a different decision at the end of the story as opposed to the beginning.
By way of example, Lost was full of character development. Jack Shephard at the end of the story made several decisions he never would have considered at the beginning. On the other hand, Star Trek: The Next Generation ended with the same Jean-Luc Picard as it started with. Sure, he had some new experiences, but by the time the credits rolled on the last episode, he was still a man who talked first and shot later, an intellectual with a bit of a temper, and a bit resistant to change in his crew and on his ship.
Did the difference make one show better than the other? I'd argue no; I enjoyed both immensely. But it meant that the nature of the conflict was very different. Star Trek was all about people overcoming external obstacles and working together; Lost was all about individuals overcoming flaws and trying to fix sometimes self-created problems. One of them could afford to have a cast composed of equal parts heroes and villains, with a great deal of moral ambiguity. The other more or less required a core group of characters who, while flawed, were fundamentally decent people who would just make the occasional misstep.
Now try running the two of them together. Either way, it doesn't really work. Transport Lost's cast into Star Trek; you wind up with a horribly directionless crew that's so busy pursuing conflicting agendas that nothing gets done. Put the crew of the NCC-1701-D on the island and everyone winds up sitting around comfortably until rescued, with no real internal conflicts to keep the show moving.
The trouble is that both of these outlooks start from very similar points. In both cases you start off with a cast of capable but flawed individuals, generally with the expectation that these flaws will eventually cause some problems. The interesting part is in the telling, and it's only there that you realize that while your flawed character is meant to stay flawed and overcome interesting obstacles, your roleplaying companions are focused on developing characters and building past those flaws in a long-term sense.
Not that either side is absolute, mind. No one expects a flawed character to become a perfect demigod after a bit of roleplaying, nor do people who stick with arcs expect a character to remain wholly unchanged through everything. They're tendencies, though, and when you get right down to it, they're at odds with one another.
So what can you do? The truth is that my usual suggestion to just roll with the punches doesn't always work as well here; roleplaying is an intensely personal thing, and if you're not comfortable with the style that everyone else likes, you're going to have a much harder time feeling invested in the stories of others. And the option of splitting the group into multiple groups based on something this little is a really bad idea. (Although it happens -- I suspect it's one of the causes of subtle RP drama that no one really likes to talk about, although I've only seen it in action and observed it as such a couple of times.)
No, the best thing you can do is to recognize what is happening and bring it up for discussion. Make clear that while you enjoy the people around you, they've got a different style than you do, and you want to work something out so that OOC clashes in wants aren't going to interfere with actually playing the game. It might require some revision in character concepts, but if you've got a good group, people will usually be happy to meet you halfway if you'll do the same.
It might lead to a little drama, and if you're the only one who likes one style over the other, or if the people who like the other style don't recognize it as such, there can be some conversational landmines. But talking to people out of character and communicating effectively is a topic for another week.
Next week? No, next week I want to take a look at another split (or the lack thereof) between you and your characters. Until then, feedback can be sent to firstname.lastname@example.org or left in the comments, just like always. (Yes, this column is really big on the character arc. It hasn't changed much.)
Every Friday, Eliot Lefebvre fills a column up with excellent advice on investing money, writing award-winning novels, and being elected to public office. Then he removes all of that, and you're left with Storyboard, which focuses on roleplaying in MMOs. It won't help you get elected, but it will help you pretend you did.