Find the unique twins
Jelly, 7 bytes

fċ@ÐṂ;Ṁ


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How it works

fċ@ÐṂ;Ṁ  Main link. Left argument: A. Right argument: B

f        Filter; keep those elements of A that appear in B.
   ÐṂ    Yield all elements of the result for which the link to left yields a
         minimal value (2).
 ċ@        Count the occurrences of the element...
     ;     in the concatenation of A and B.
      Ṁ  Take the maximum.