I am familiar with both of them, but uncertain as to which one I should implement on an OSPF network.
I'm leaning towards the static default route for an edge router bc it's easier to configure and requires less resources.
I would like some opinions please. Thanks in advance.
I would go with an NSSA design instead. The reason is that a Stub area or Totally Sub area does not receive external routing information from the backbone, which is great for the reduction of LSDB size, but this restriction on type 5 LSAs cuts both ways, because a stub area cannot introduce external routing into the backbone either. For example, you can not redistribute from another routing protocol like EIGRP, RIP, etc... into OSPF. A not-so-stubby area (NSSA) addresses this issue by defining a new LSA type (type 7) that allows an NSSA to support the presence of ASBRs and their corresponding external routing information. By default, type 7 external LSAs are converted by the NSSA’s ABRs into conventional type 5 LSAs for flooding throughout the routing domain.
I might be misunderstanding your question, but it seems you are asking whether to run OSPF or use static routes. When you specify an area as totally stubby no LSAs are sent to that area. Only a default route is injected by the ABR. No need to manually configure a default route at the stub router. If you were to do use static routing the upstream router would also need static routes back to the stub router and those would need to be redistributed back into OSPF.