The best platform to play games on is the PC or a laptop since you are posting in the laptop sub-forum. Both PS3 and XBox 360 are pretty dated systems and are weak even compared to laptops. Hardcore gamers recommends playing on a desktop rather than on a laptop because you can get better performance at a lower price than most laptops. Unless you are looking at the real cheap laptops, in that case it probably will cost a bit more for a desktop, but you'll also get better performance.
Why laptop/PC? Simple. Community create mods for the game which improves graphics. Gives you more armor, weapons, powers. Add new monsters, quests, towns, caves, castles, dungeons, cities. Change the style of game play to make it easier, harder, more realistic (you must eat and sleep). The possibilities are only limited by the modder's imagination. However, not all mods are compatible with each other, not all modders have the same level of competence creating mods which can cause the game to crash.
Are you going to be able to play Skyrim flawlessly on a laptop/PC? No. There are still bugs that can cause the game to crash. And stated above, community created mods can also crash the game.