I would try to get away from needing to rely on things like "order". Which is why I suggest you use a hash, and building a unique key to find the matches between the two lists.
Again, finding the criteria that make a match between the two lists is something only you can know. But if you have found and formulated what makes two elements "identical" in your case, it makes finding the match much easier, because then you can use that "identity" as the key into a hash and check whether an element with that key exists or not.
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