Old topic - but an important aspect not covered here is that a "renewal" can generally be actioned within a 90 day window - from 60 days prior to 30 days after expiry. Ref: https://ie.godaddy.com/help/renewing-my-ssl-certificate-864
A "rekey" on the other hand requires the certificate to be updated within 72 hours. https://ie.godaddy.com/help/rekey-my-certificate-4976
The question to ask is "are we concerned that the key may have been compromised?". If the answer is "No" then a renewal requires less time and is easier to coordinate, especially when involving multiple parties.