Probably is not a matter of what can/can't be done, but how.
For instance both have editor surrounded with dock panels for project, classpath, output, structure etc. But in Idea when I start to type all these collapse automatically let me focus on the code it self; In eclipse all these panels keep open leaving my editor area very reduced, about 1/5 of the total viewable area. So I have to grab the mouse and click to minimize in those panels. Doing this all day long is a very frustrating experience in eclipse.
The exact opposite thing happens with the view output window. In Idea running a program brings the output window/panel to see the output of the program even if it was perviously minimized. In eclipse I have to grab my mouse again and look for the output tab and click it to view my program output, because the output window/panel is just another one, like all the rest of the windows, but in Idea it is treated in a special way: "If the user want to run his program, is very likely he wants to see the output of that program!" It seems so natural when I write it, but eclipse fails in this basic user interface concept.
Probably there's a shortcut for this in eclipse ( autohide output window while editing and autoshow it when running the program ) , but as some other tens of features the shortcut must be hunted in forums, online help etc while in Idea is a little bit more "natural".
This can be repeated for almost all the features both have, autocomplete, word wrap, quick documentation view, everything. I think the user experience is far more pleasant in Idea than in eclipse. Then the motto comes true "Develop with pleasure"
Eclipse handles faster larger projects ( +300 jars and +4000 classes ) and I think IntelliJ Idea 8 is working on this.
All this of course is subjective. How can we measure user experience?