What's the difference between the PC, 360 and PS3 versions of Skyrim?

The PC will support mods:

Bethesda's fifth Elder Scrolls game, like Oblivion before it, will allow for extensive player customization, according to the developer. "We've always been impressed with what the community has done with our tools," a rep for the company said on its forums, revealing, "Like the Elder Scrolls Construction Set for Morrowind and Oblivion, we plan to release [a] Creation Kit so you guys can mod Skyrim."

The immediate predecessor, Oblivion, has seen countless mods -- everything from new characters to online play. We can only imagine what the Skyrim community will manage to create while we wait for Bethesda to finish the most ambitious Skyrim mod, Fallout 4.

Source: Joystiq

The PC also supports console commands which can be convenient if there is a bug with quest items.

The Xbox 360 has the first 2 DLCs exclusively for 30 days.

Source: Gamespot

As far as I've found all three versions support achievements/trophies.

PC:

• Limited graphically only by the power of your system. I have no evidence to support it will be prettier than on the PS3, but if you have a sweet vid card and force 8xAA, I 'assume' it CAN look prettier.
• Modding. Ability to load mods, make mods, share mods, mods mods mods. Can add infinitely to your gameplay, and sometimes they even alter huge elements to were it is nearly a different game altogether.
• Steam integrated, which for me is a perk as I love their built-in chat system where I never have to leave the game. Adds just enough of a social aspect to keep me gaming nonstop for hours.
• The mouse is a huge advantage for aiming, even against a great console controller. Some of this has been negated due to poor interface choices, but I still found aiming the attacks much easier. Some may argue the mouse vs. controller issue, but for me it was obvious in this game. Might not be for you.

PS3:

• Everyone has the same game. Plays the same. No mods beyond whatever DLC they provide(which, like the PC will be 30 days after the XBOX gets it). You won't have to worry about the performance, as it was made to run well.
• The menus seemed designed more for console than the PC. While it didn't limit me, I imagine some of the interface would be easier to navigate.

XBOX360:

• Will have slightly (from what I've seen) less graphics detail, but I honestly just can't see a huge difference in any of the versions. But I would assume the textures and the maybe the view distance will be lower quality/smaller than on PC for sure, and possibly PS3.
• The first few (3 I think) DLC will be on XBOX360 for 30 days prior to any other system.
• The menus seemed designed more for console than the PC. While it didn't limit me, I imagine some of the interface would be easier to navigate.

Summary:

While you didn't ask for 360, I threw it in anyway. I have personally only seem this/played it on PC and 360. So I am not 100% sure on how they did with the graphic quality on PS3, but the system itself CAN handle more than the 360 so I would assume they took advantage of that at least a little bit.

Some of my reasons were personal, so take those for what they would mean to you. As someone who loves Steam (hacked or not), the social integration is much more natural than the consoles to me. (TO ME)

In the end, the only wrong answer is to not buy the game. Buying it on any console or the PC is going to bring you hours and hours of entertainment.

This comes down to personal preference, I would say the biggest perk on each side is;

PC

• If it is anything like Oblivion, then modding support will be a big draw here. PC users always enjoy more modding support for their games then their console brothers. If you want to extend your core gameplay experience there is no question.

PS3

• The biggest advantage here is that, if you don't have a powerful PC you can still enjoy the game in its full glory. The game does require some steep requirements to look good on PC, so you can save your money by going the PS3 route.

Outside of this, it comes down to what you enjoy gaming on the most. Note that Skyrim is a console port for PC, so the controls are a little bit more sluggish since they have a controller first in mind. However, that also means you can simply plug in a controller to your PC and play that way if you like.