Hi,
The s_vi cookie is the old, pre-visitor id service user identification... it was set per domain, and that means that not only would the visit be different, so too would the user...
Now, if you also have an ECID, then the visit and visitor should defer to that, as the ECID should be set against your Organization (and not just the site)... s_vi is still often set as a backup, but ECID should be the main identification.
If you are seeing two s_vi cookies on the same site (with different domains), it probably means that you have some shared resources being pulled into your site... but Adobe would just read the s_vi that belongs to the site you are on.... now, if you have it set against the root domain (.domain.com) and against the www (www.domain.com), I am not sure which one Adobe will take as the primary... but you should see the s_vi value as part of the tracking, so you can see what is being sent to Adobe as part of the identification.