Since isEmpty() checks if the length of the String is 0 and "" is the only String with length 0, each String for which isEmpty() returns true would also return true to .equals(""). So technically, they do the same thing.
There might be a minimal difference in performance, but I wouldn't bother about that at all (I'd be very surprised if it were noticeable in production code).
Another difference is if you wrote "".equals(someString), then it would be "null-safe". In other words: if someString was null, this construct would simply evaluate to false and not throw a NullPointerException. If, however, you have someString.equals("") then this would not apply.
The most important difference is how it's read: isEmpty() makes the intention very clear: you want to treat empty strings differently. .equals("") is ever so slightly less clear ("if that string equals that other string, that happens to be empty").