I'll define the terms, and then give you some of the most common reasons people give for why they chose (or didn't choose) a particular method. I'm not saying these reasons are right (or wrong), I'm just saying these are the reasons people give, and you can evaluate their rightness or wrongness for yourself.
Pantsing - Writing by the seat of your pants. It's the same as doing anything else by the seat of your pants (if English is not your first language, and you are unfamiliar with idioms, I AM SO SORRY because this one is really weird.) You start out with only vaguest idea of where you're going, and you let the journey shape your path as you go. Or, in the case of writing, you let the story shape itself.
- The thrill of "discovering" the story. Many people say it's akin to reading, just you're the one telling the story. It's fun to say, "Ooh! It'd be crazy if THIS happened now!" and then make it happen.
- Freewheeling feels more artistic and creative. Feeling like your characters are speaking to you, or your muse is leading you on, or any of these things is very liberating. Even a dedicated plotter loves the chance to free-write once in a while, just let the mood take them wherever.
- Doesn't require any special planning or training. You don't need to know anything special about the three acts of a story, or pacing, or any other technical aspects of constructing a story. If you read a lot, and you can feel "something needs to happen soon" then you can pants your novel. Anyone can dive in.
- It's easy to get stuck. It's easy to get caught up in the fun of a story and not realize that you have no possible way to tie things up. Or that you put your love interest in two places at once. Or you killed off your villain halfway through the book. It's also really easy to write twelve thousand words of crap before you realize you're going in the wrong direction.
- Drafts are super messy. Plot holes, inconsistencies, tense issues (as in, switching from past to present tense), appearance and disappearance of characters (and not in the good way), and a whole host of other problems will present themselves more often when you write without a plan. Pacing is more likely to be wrong, and you're more likely to find huge, sweeping scenes of absolutely nothing useful at all, because you got caught up in the moment and just kept writing without a plan.
Plotting - Creating an outline before beginning to write. Outlines can be detailed (I'll spend 3,000 words in chapter four on this scene, it will have sexual tension, an almost-kiss, and three jokes) or not (First they'll travel to the Forbidden City, and along the way they'll pick up a hitchhiking ghost. Next there will be a fight scene and the tall guy will lose a hand.) Some people plot chapter by chapter, or by how many words need to be dedicated to a particular scene or plot point.
- Writing time is all word count. You have a plan. You know you need to write a scene where the villain confesses his evil secrets to a secondary character so she can eventually betray him. You have one hour. For that one hour, you will do nothing but write the scene that you need. If you don't have a plan? You'll spend time writing stuff you won't use, going back an re-reading previous stuff, tinkering with editing, or writing a scene that takes the story in a wrong/weird direction.
- Editing is smoother. You'll still make changes, some of them major, but it will be unlikely that you'll say, "What? This character disappeared after chapter six, and then I introduced somebody else kind of like him, and why do I have twelve pages of dialog that has nothing to do with this story?" Also, because you outlined specific scenes, it's easier to cut and paste them if you need to move them around. Without that outline, it's more likely that you have scenes interwoven together in a nonsensical fashion.
- It's like building a puzzle. Piecing things together without the messiness of dialog or setting or sensory details getting in the way. It's easier to see how the plot fits together.
- Stifles creativity/artistic freedom. Lots of people feel like planning their art is a little like painting by numbers. Putting the story into boxes or outlines or timelines or anything else involving straight lines is boring and not artistic.
- Takes a lot of time before you get to the fun part. Spending time on an outline is time spent not actually writing. It's technical and much less fun than spending time writing a kiss or a sword fight. Especially since most dedicated plotters will plot before they write a draft, then will use a beat sheet after each subsequent draft to check their pacing, an awful lot of writing time gets dedicated to not writing the story.
The Combo - Of course, many people combine plotting and pantsing. I pantsed my way through a 40,000 word rough draft with almost zero dialog or world building, just plot and character introductions. Guess what? That's an outline, albeit an unconventional one. It was easier to make changes to that doc than it would have been to make changes to a full draft.
Some people write chapter-by-chapter concepts with no details, some people pants the first half of the book to get to know their characters and then create a detailed plot before they continue.
On this blog, and on many other resource blogs, you'll find writers talking about their methods, as well as how and why those methods work.