Get the fat one, if you did'nt get anyone yet. The benefits of the slim aren't really that great.
The fat has a better screen.
The slim comes with 1GB on-board storage, but that's not enough for pretty much anything. I got the 4GB bundle with the fat and it still isn't even close to enough. Not to mention that 1GB storage becomes completely unusable when you have a memory card inserted. So unless you plan on playing 1-2 PSN games at a time and never buying a memory card, the 1GB storage means nothing.
The slim has a more mainstream charging port. But I have a propiertary port on my phone, and I've never lost it or needed a new one. So this isn't that big of a deal.
The slim is thinner. I haven't held the slim, but the fat one already seems too thin for me, my hands cramp within a couple hours of gaming. Because of this, I don't have a problem with battery life either. I just charge it while my hands rest.
There are no new features with the slim. In fact, there MAY actually be less. The fat has a port on it that the slim doesn't. Sony removing this port might mean that they have no use for it, but you never know, some obscure Japanese attachment may come out in the future that's only compatible with the fatty.