Earl E. _ first off, I gotta tell you that your moniker just put me into thinking "Wile E. Coyote" - like you're giving up hunting roadrunners for lobsters now.
Eels don't bite all that hard, but their teeth point inwards. They chomp and then can start twisting themselves. They can leave a real jagged tear in your skin that is alsmost guaranteed to become infected. My wife has a friend who had her fingertip bit off by an eel on her very first dive and her ex lost part of a finger to another eel. So I'm real careful around her.
Eels pretty much leave you alone unless you go riling them up. Except for those nasty green ones, they're all pretty shy and retiring. And if you see one, maybe you don't need to go pointing at it too closely.
If you do managed to get chomped though, make sure you have an Acme Eel Remover though.