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