Skyrim probably has more going for it in the long run, especially with the very active modding community; not to mention the Creation Kit was finally released the other day. I'm not far enough into Amalur to say whether or not it's setting is as rich and expansive as The Elder Scrolls series, but let's just say it's very unlikely that it does. But yes, Skyrim is more than likely to be the game with more value; nevertheless, both games are quite good in their own ways and certainly worth picking up at some point.
Still, I think it's probably worth looking at the finer points to determine which you prefer.
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Skyrim's main advantage (apart from the near-limitless possibilities mods can add to it) is it's sheer scope; it's a massive game, with far more content than anyone could reasonably expect out of a game. The level of interaction with the setting is another strength of the series, and there's countless random (and probably silly) things you could do. However, the actual gameplay can be rather lacking; while still much better than prior entries of the TES series, it has the age-old RPG problem of "meh combat".
Which brings us to Amalur's main strength -- good gameplay. Not top-notch gameplay, but certainly one which wouldn't be bad for a full-on action game. The best gameplay ever seen in an RPG, as EA's routine hyperbole would say? Not really, but much more fun than the majority of RPGs available. The one downside to the gameplay is that you really want to get a controller for the PC version (an Xbox 360 controller works fine, driver for it is a free download; if you only have wireless controllers, I'm not sure if a particular piece of hardware is needed or not), because the gameplay translates very poorly to the mouse and keyboard; at least Skyrim has mods to fix the issues with the PC interface. Anyhow, Amalur is more fun to play... but it's (probably) not the better overall experience in the end.
And since it was mentioned, there's also Dark Souls. Both of the above games get a little too easy, while this one does not; when enemies get tougher in the "New Game Plus" mode, little else needs to be said. This particular game has earned a lot of praise lately, and it's well-deserved. This is a game with a lot of challenge, and provides a sense of satisfaction when you overcome each obstacle; something very rare these days. However, it's the easily the most frustrating of the lot; this isn't exactly a "fun" game, but there's something intangible which makes those frustrations worth it in the end. This is a game which can never be outright recommended due to it's raw difficulty; but those who enjoy it, end up loving it. The (current) lack of a PC port may also put some people off, as it's only out on consoles.
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Overall, Skyrim's best recommendation. The other two games are still worth picking up, or at least Amalur is; not everyone can handle Dark Souls.