The Fat PS3 is more vulerable to overheating and getting a Yellow Light of Death. Some of the PS3 fat models are backwards compatible with PlayStation 2 games. It includes a bit more features that were removed in the later revisions, to cut costs, because they thought there wasn't a point in it, etc. Some fat ps3s also have more usb ports, most PS3s have only 2, but some models of the fat PS3 include 4. The fat ps3 also has other storage ports, like SDIO/MMC, Compact Flash, Memory Stick, and SD cards that were later removed in the newer models of the PS3. Another thing with the Fat PS3 like Pinhedd mentioned, was that the HDMI transceiver is specced to HDMI 1.3, which means that theres no 3d, and the fat models can't stream Dolby Digital TrueHD or DTS-HD Master audio straight into the receiver, but it can decode them internally. The fat ps3 can also be jailbroken, to include much more features, like install packages, have debug tools, and more.
I think that the newer models, which are the slim and super slim boot much faster and are much more quieter. Some PS3 slims have backwards compatibility for PS2 games, but only some. The super slim, I believe doesn't have any compatibility with PS2, although, ALL ps3s, including the fat support PS1 games. Some PS3s support PS2, but ALL ps3s support PS1 games. The super slim cannot be jailbroken, only the slim and fat. The slim and super slim are much more quieter and slimmer than the ps3 fat, the super slim is the quietest.
I also just noticed that you were asking for what ps3 should your friend buy for jailbreaking. Well, you can read all this info and see which one is best. None really make a difference, it doesn't really matter, just make sure the super slim is the one he doesn't get, as it isn't capable of being modded.