Both required a good initial configuration, but when "issues" occurs like link flaps or ISP outage (when MPLS fails), Dynamic may affect Router performance (CPU, Memory, etc).
Using Dynamic Routing; if you have no backup link or you dont have a proper failover configuration with correct threshold, the network updates will cause router performance degradation. It constantly will try to reach destination via default gateway.
Using Static Routing; If you have not a recovery plan or a back door to enter the remote router, you will have zero access to that device until link or issue is restored. Packets will be forwarded to a dead route.
For both, Initial design and configuration is the Key, when issues happens troubleshooting is a nightmare when things are not well done.
