In this kind of Setup, I would always recommend to run a routing Protocol at the CE router with the Provider. and Since the Provider has two Options only, then I would say run BGP.
Let me give you the disadvantage of using Static, initialy you have the Corp Office dual Homing to both DC1 and DC2.
Lets consider the main link was through DC1, a sudden failure took place on the link between CE and PE of Corp Office, the Provider is not detecting it rapidly because the Arp-cache still contains an ARP entry for this link, as a result the PE still sends a static route pointing to the Corp for this link to the Edge LSR connected to DC1 which allows DC1 still believes the link is active and would still use it to forward all traffic destined to the Corp Over it and the Traffic eventually gets dropped. this Symtom continue till the Arp-cache is timed out which happens every 4 hours in a Cisco router or Gets manually cleared, Here I specifically talks about Ethernet WAN, with Serial WAN links , a failure once detected the Interface would Go down and the Static route wont be considered, Unlike the case of Ethernet WAN links.
As a result of the above, the Corp would not switch to the Second Path to DC2 rapidly.
While, if we are using BGP, a failure once detected on the WAN link, the Upper Link layer Protocol gets notified and reachability between BGP peers would fail, which allows the Corp Office to immediately Switch to the Secondary Path through DC2.
This is the main difference between using Static and BGP in a dual homing Scenario which requires a fully redundant Solution and its applicaple in your case. So the Best Option is to use BGP as your routing protocol with the Provider.
Regards,
Mohamed
