Firstly I'd say that it's not impossible that Qadisiyya was earlier than Yarmouk: possibly as much as several years earlier, if one looks at some Iranian sources. The chronology of the decade is very confused.
From my sketchy knowledge, I think that even with an Arab defeat at Qadisiyya, the Sasanians are probably still doomed to be replaced by a Parthian dynastic family: the cracks were appearing as early as the 590s, and it was only the military successes of Khusrau II that kept things just about in check. Iran is still going to be a mess here, so I'd foresee probably a period of civil war and confusion before a new Iranian state of some sort, be it Persian or Parthian, emerges out of the ashes in the 640s. This state is unlikely to be truly Zoroastrian as we understand the term.
On the Roman side, a victory at Yarmouk and decisive repulsion of the Arabs from Syria and Egypt probably just switches the focus of the Emperors on maintaining their positions in Italy and Africa in the face of major theological dissent. All Emperors of the period were extremely concerned to find a formula that would be acceptable to all sides in the Chalcedonian debate to fulfill their role as God's regent on Earth, and contrary to popular belief it tended to be Western clerics who caused the most trouble in this. So I'd foresee more active, Constans II style activity, arresting Popes and such. Plus attempts to restore some measure of control over the Balkans in any respite that might emerge from an Iranian civil war.