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While filecmp.cmp and filecmp.cmpfiles allow a shallow option to be specified to invoke a more involved comparison of files, filecmp.dircmp does not. It is limited to shallow-only comparisons. 
This could be solved quite easily by adding a shallow keyword option to dircmp then changing the phase3 method to the following.
 def phase3(self): # Find out differences between common files
 xx = cmpfiles(self.left, self.right, self.common_files, self.shallow)
 self.same_files, self.diff_files, self.funny_files = xx

Thanks for the report. Unfortunately 2.7 is closed to new features and the module is removed in 3.x, so there is nothing to do here.

filecmp is still there in Python 3.3 Alpha 3. I can't find any reference to it being deprecated.

Lennart, I saw your response on StackOverflow ;-).

+1 for this.
Whether or not this feature is implemented, I think the documentation should state that directory comparisons are done using "shallow=True". I created issue 15250 for this.

Allowing dircmp() to accept a file comparison function is another option to consider that may address more needs going forward. shallow=False could be achieved by passing lambda a, b: filecmp.cmp(a, b, shallow=False).

Add input parameter 'shallow' to dircmp.
Use it in phase3 and phase4.
Document it in filecmp.rst.
Did not modify test_filecmp.py.

Thanks for the patch @planet36, however I think this is sufficiently large a change that we should also have a test case for it.
I'm also retargeting this to the current open branches for feature work - 3.6.

Bah, wrong stage. patch review.