That would be true in both cases. A full grown cat weighs as much as a bald eagle does and can twist enough to put up a fight. Both sides would have a bad day. In that size range the only thing worse for a bald eagle to try and prey on is a full grown fisher which have been known to kill lynx, coyotes, and young deer despite not weighing much more than a cat (though they'll certainly go after the younger ones).