If you have E2, then closest ASBR is only chosen if there is a tie in the metric. That should always be the case if you redistribute with the same metric. You could redistribute with different metric if you want one path to always be preferred.

So E2 routes with same seed metric almost behaves like E1. If you have two E1 routes with same metric then both will be installed. But you could have two E2 routes not being installed in case seed metric is different and cost ends up the same but one has better forward metric then only one would be installed. So there is a minor difference still between E1 and E2.

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Now within the scope of OSPF, think of the E2 route selection process: OSPF chooses the best exit point based on the external metric and uses the internal cost to ASBR as a tie breaker. In other words, OSPF performs “cold potato” routing with respect to E2 prefixes. It is easy to turn this process into “hot potato” by ensuring that every exit point uses the same E2 metric value. It is also possible to perform other sorts of traffic engineering by selectively manipulating the external metric associated with the E2 route, allowing for full flexibility of exit point selection.

Finally, we approach E1. This type of routing is a hybrid of hot and cold routing models – external metrics are directly added to the internal metrics. This implicitly assumes that external metrics are “comparable” to the internal metrics. In turn, this means E1 is meant to be used with another OSPF domain that uses a similar metric system. This is commonly found in split/merge scenarios where you have multiple routing processes within the same autonomous system, and want to achieve optimum path selection accounting for both metrics in both systems. This is similar to the way EIGRP performs metric computation for external prefixes.

So there we have it. While it is technically true that “OSPF routers do not add any internal OSPF cost to the metric for an E2 route”, both the intra-area and inter-area cost can still be considered in the OSPF path selection regardless of whether the route is E1 or E2."