It's still odd though.  Why does object() == Anything() pass control to
the right hand side, while (lambda: None) == Anything() doesn't? 
There's no definition of equality in PyFunction_Type, so it would seem
to fall back on the definition in PyBaseObject_Type, which I would
expect to return False from the code in object_richcompare()...

[...gdb...]

OK, here's the solution of the mystery.  do_richcompare() ends up taking
the swapped code path for object() == Anything(), but not for function
objects.  This is because Anything() is a subclass of object, but not of
<function>.

Perhaps the solution is to change object_richcompare() to return
NotImplemented instead of returning False?  Or perhaps even remove
object_richcompare() altogether, since it doesn't do anything that
do_richcompare() doesn't know how to do...