So I'm starting to think I have a different opinion than a lot of people: for most situations on a large ship that has Contain, RBD is the much better choice than ECM.
ECM is good when you are going to be taking more than 4 damage multiple times over the course of at least two turns, perhaps three. In all other cases, I think RBD is better.
Damage cards are more expensive to ditch than just recovering or moving shields. If I'm expecting to take damage, I often have an Engineering command stacked. With RBD, I don't have to worry about an accuracy on a Redirect and can just let some of the damage through. Then the Engineering can either recover the shields lost or move shields if that makes more sense, and the RBD discards most or all of the damage cards.
RBD is useful for offensive Engine Techs or when you expect to be rammed.
ECM is useless if your opponent doesn't roll or create accuracies.
RBD is useless if you don't take damage cards or if you die in a single turn.