Was there ever an incident where a eagle has picked up a small dog that weighs more than 5 lbs?
Probably, eagles have been known to carry off something as large as goats and baby deer.
It depends on the eagle species. A bulldog would win any small eagle species. But if a small eagle hits the bulldog's skull, the dog would be hurt. If the bulldog fought with a large eagle species, it would be close. If the eagle is on ground, it would be torn apart. If the eagle is in the air, it wins.