Against a guy like Lucic, no, he's not a good fighter...
But, he's a relatively small guy, and if he stays in his weight class and goes up against players of similar importance to their team (top 6 forward/top 4 d-man) hes a pretty good fighter.
People don't like him because they think he should fight guys like Lucic, or guys that are in the league primary bc of their fighting ability.
The Eager fight...Bieksa was way smaller, and Eager bearhugged him and body slammed him to the ice. I think Bieksa gives up at least 30+ pounds to Eager.
What would I say about his fight skills (at his peak, not now): he knew what he was doing with his fists, but was never a heavyweight or anything like that.
His class of fighters would be guys like Carcillo and Avery.