Do two numbers contain unique factorials?
Jelly, 7 bytes

Æ!ṠḄ&amp;/¬


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How it works

Æ!ṠḄ&amp;/¬  Main link. Argument: (x, y) (pair of integers)

Æ!       Convert x and y to factorial base.
  Ṡ      Apply the sign function to each digit.
   Ḅ     Unbinary; convert each resulting Boolean array from base 2 to integer.
    &amp;/   Reduce the resulting pair of integers by bitwise AND.
      ¬  Take the logical NOT of the result.