Preamble to my answer: My use of Eclipse is limited. We needed a Java IDE to work on both Windows and Mac and the Mac port slowed down day by day. This was years ago and I'm sure it's OK now. But that is what got us to switch to IntelliJ and we've been happy with it.
Now for my answer: One big difference I haven't seen mentioned yet is that tech support is better with IntelliJ/Jet Brains. We send an e-mail to JetBrains and get a definitive answer back in less than an hour. Looking for answers to Eclipse problems results in the usual, "You stupid idiot" answers (usually a small number of the replies) along with the much larger number of insightful, helpful replies. But it takes some sorting through to get the real answer.
