Decrypting a vigenere cipher with a reused one-time pad
The crib-drag attack applies with a different operator.

p1 = AtextencryptedByFirstPassword
p  = HelloHelloHelloHelloHelloHell
c1 = hxpihlrncmwxpopfjtcgatldgdsco

p2 = ASecondEncryptedTextBySecondPassword
p  = HelloHelloHelloHelloHelloHelloHelloH
c2 = hwpncuhpyqycaeskxpihicdpqvroaozwhzfk


When you $c_1 - c_2 \bmod 26$ you will have the same problem as many-time-pad. This subtraction will remove the key. 

 c1[i] - c2[i] = p1[i] - p2[i]


But this time instead of $\oplus$ we will have plus modulo 26. 

 c1 - c2 = azafvjqcwecflqdfowgbijsmkszmm