Using version 6.x-2.10 of Login destination (2010-Mar-19) with version 6.x-1.4 of Persistent login (2010-Jan-08) gives the two following scenarios:

* The user has not a persistent cookie stored: persistent login won't work until Login destination is disabled
* The user has a persistent cookie stored: persistent login works but there is a case when the wrong user logs in, which is
1) Log in as User A, persistent
2) Close the browser
3) Open the browser, User A is logged in. Log out
4) Log in as User B
5) User A is logged in.
Persistent login logs in User B at 5) if Login destination is disabled