I just rewatched 'For the Cause' and it occurs to me that Sisko's extreme dislike of Eddington in particular - as opposed to the Maquis in general - isn't just a result of the fact that Eddington 'beat' him, or even that Eddington's betrayal happened on Sisko's watch. It was also a result of the way in which Eddington engineered everything: trying to push a hard line against Kassidy while he himself was far deeper involved than she was, and even using her as bait to get Sisko off the station.
Finding out within a few days of each other that both of them were helping the maquis right under his nose must have been a major blow to him. I'd imagine, in a lot of ways, Kassidy's betrayal hurt far worse than Eddington's, but, especially after she came in voluntarily, he couldn't help but transfer the bulk of his anger and resentment towards Eddington. And Eddington, with his ridiculous over-righteousness 'you're worse than the Borg' certainly did make it very easy to do so. It would've been easy for him to unconsciously blame Eddington for exposing Kassidy.
It could have even been a part of his own internal doubts about Federation policy re: the Maquis, with Kassidy (who was shipping medical supplies) representing an idea of the Maquis he had a hard time condemning, and Eddington, with his terrorist tactics and threats of further assaults on the Federation, representing an idea of the Maquis he could only despise. The fact that Eddington's Maquis won out over Kassidy's is what ultimately brings him down to his extreme anti-Maquis view.
Sisko pretty much says it himself that it's for personal reasons:
"He worked under me for a year and a half. I saw him almost every day. Read his reports. Had him to dinner. I even took him to a baseball game in the holosuite once. And I never saw it! It's my job to be a good judge of character, and what did I do? Not only did I not see it, I put him up for a promotion.
"He played his hand well.
"He played me all right. And what is my excuse? Is he a Changeling? No. Is he a being with seven lifetimes of experience? No. Is he a wormhole alien? No. He's just a man, like me. And he beat me!
, discussing Eddington while Sisko punches the bag
Sisko's reaction to Eddington's betrayal comes off as irrational when compared to his reaction to Cal Hudson.
Sisko and Hudson had known each other 20 years by the time of the 'the maquis pt 1'. Not only did Hudson shoot Sisko but engaged him in ship to ship combat, which could have resulted in Sisko's death even if that wasn't the intention. Sisko then lets Hudson go. Does Sisko go under cover, does he take runabouts to try and track Hudson down? No, Sisko just leaves him be and probably laments a broken friendship.
Even though Sisko had a friendship with Eddington, they weren't best buddies and Eddington wasn't part of Sisko's inner circle. So why did he get so vengeful and make it personal, because Eddington kept outsmarting him. It just makes Sisko look petty and unprofessional.