There are pros and cons to both places. I've had a lot of experience with both of them, so here's my list.
Fanfiction
Pros
* Easy to use.
Some may disagree, but I have never had a problem accessing or searching Fanfiction. It's the simplest thing in the world to post a story there, and frequent site updates mean that any bugs or issues they have get fixed pretty quickly. These guys really know what they're doing.
* Well organized.
For a site that caters to every type of permissible fan fiction out there, it could easily have become a total mess--but it's not. The library is organized by source (Anime, Books, Movies, Games, etc.) with a very efficient search function, and shows you more stories in less space. Because of that, it's just more fun to surf stories on Fanfiction: "hmm, that one sucks, that one sucks, that one sucks, hey this one looks good!"
* Convenient to other fandoms.
If you've read enough pony stories for today, no problem! You can be reading Harry Potter, Digimon, or (shudder) Twilight in the very next minute. Fanfiction has everything. Some shows and movies have niches there that you won't find anywhere else.
Cons
* Boring design.
In this modern Internet age, Fanfiction's main page looks like something out of 1995: all text, no pictures, few colors. On one hand, it's nice to have a site that is still simple, unpretentious, and totally content-driven. But it doesn't do much visually to draw the attention of new authors.
* Harder to get feedback.
You would think that Fanfiction's larger audience equals more activity and a better chance to get noticed, but it doesn't always work out that way. The site is like a big city with a ton of writers just going about their business, too busy to leave many constructive reviews. In comparison, FIMfiction is like a small town, with comment sections that are more active and more fun to read--though not always more helpful.
FIMfiction
Pros
* Looks great.
FIMfiction has always been a more attractive and visually appealing site than Fanfiction. The fancy layout, the bright colors, the feature box...everything about it screams "modern" and "professional".
* Sense of community.
Fanfiction still has a primitive and disconnected posting system; FIMfiction is far better in this area, with thriving groups committed to every genre of pony story you could want. Everyone is intertwined and feels part of something--a huge plus for all authors, but bronies in particular.
* Exclusive to bronies.
Some of us are still uneasy about using sites where they might find unfriendly users. But FIMfiction is maintained by and for people like us, and that means a lot.
Cons
* Shakier history, with more technical problems.
When I started using it three years ago, the search filter was a disaster. I could rarely find a specific story unless I Googled it, and no search would return more than 20-40 stories at once, even if I searched for something really popular like PinkieDash. It was tremendously frustrating. The search works a lot better now, but in general FIMfiction still has more issues on a daily basis than Fanfiction.
* The screening system.
Don't get me wrong, it could be a pro if the mods consistently followed the criteria they laid down, but the fact that it's done so subjectively means that some good stories will be rejected on a technicality, while a lot of horrible ones (even ones that don't meet "a basic level of grammar and spelling") still get approved.
* Longer learning curve.
I figured out how to use Fanfiction very quickly when I was just getting started on "the Internetz." I joined FIMfiction after 12 years of experience writing online, and their subscription and publishing systems were massive headaches. It took weeks to really figure them out.