Think of an eel as the striped bass equivalent of your favorite food - I could be full, but if someone offered me a piece of cheesecake I would usually say yes.
The main advantage of eels is castability and logistical ease. You don't need a live well, and they stay on the hook.
However, the last two seventy pound fish I heard of in these parts fell to menhaden heads fished inside harbors.
The short answer is that they are both excellent.