Should the JUnit message state the condition of success or failure?

I rarely even bother with a message, at least for assertEquals. Any sensible test runner will explain that you were using assertEquals and the two things which were meant to be equal. Neither of your messages give more information than that.

I usually find that unit test failures are transient things - I'll rapidly find out what's wrong and fix it. The "finding out what's wrong" usually involves enough detail that a single message isn't going to make much difference. Consider "time saved by having a message" vs "time spent thinking of messages" :)

EDIT: Okay, one case where I might use a message: when there's a compact description in text which isn't obvious from the string representation of the object.

For example: "Expected date to be December 1st" when comparing dates stored as milliseconds.

I wouldn't worry about how you express it exactly though: just make sure it's obvious from the message which way you mean. Either "should be" or "wasn't" is fine - just "December 1st" wouldn't be obvious.

According to the junit API the message is the "the identifying message for the AssertionError" so its not a message describing the condition that should be met but a message describing what's wrong if the condition isn't met. So in your example "objects aren't identical" seems to be more conformant.