If you read it as do any of 1,2,3,4 match any of 1,2; then the answer is Yes 1 matches 1 and 2 matches 2, so the result is (1,2):

print eigenstates( any(1,2,3,4) == any(1,2) );;
1 2
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The confusing one is eigenstates( any(1,2,3,4) != any(1,2) )

To me that reads as do any of these not match any of those. Stepping through you get

1. 1 does not match 2, so add 1 to the result.
2. 2 does not match 1, so add 2 to the result.
3. 3 does not match 1 so add 3 to the result.
4. 3 does not match 2 so add 3 to the result.
5. 4 does not match 1 so add 4 to the result.
6. 4 does not match 2 so add 4 to the result.

So the result is (1, 2, 3, 3, 4, 4), but similar states collapse, so (1, 2, 3, 4).

So all of the first 'set' do not match at least one of the second set. But that's not what you get:

print eigenstates( any(1,2,3,4) != any(1,2) );;
1 2
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Doing it the other way around, you get:

print eigenstates( any(1,2) != any(1,2,3,4) );;
4 1 3 2
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Which also doesn't make sense because 3 & 4 are not even a part of the first set. (And I don't think the order is defined, so that's not a clue.)

Which tends to imply that the result of any(set1) != any(set2) means anything from set 2 that can not match something in set one, which is all of set2. And that just seems wrong to me.

There's probably some deeply meaningful reason for that, but it is certainly unintuative. At which point I gave up trying to understand.