I think one of the biggest reasons is that Unreal was one of the first commercial engines to claim PS3 and XBox360 compatibility, but there's more to it than that.
In my opinion, one of Unreal's strongest selling points is the tool set. The Unreal Editor encompases everything you really need to make a game (excluding art generating programs like Maya or Photoshop). It can handle scripting, material creation, sounds, cinematics, level creation, and pretty much anything else you can think of. Almost everything I've done at work has touched a different part of the editor, and after nearly 4 months I still don't know half of what it's capable of.
Now, being as monolithic as it is, there's a bit of a learning curve. But even that is surprisingly small, in my opinion. I play around in the editor quite a bit, tracking down bugs or trying to find where my next feature will fit in, and usually within a couple hours I can get a good enough feel for how a particular subsystem works to at least be functional with it.
There's a lot to be said for the various portions of Unreal (though I have mixed feelings about the code [headshake]), but I really think that a great deal of its success is a direct result of its tools. An engine is only as good as its tool set; after all, you don't want your designers slogging through code all day.