SOMERVILLE — Mike Moccia and Yasser Mirza just don’t get along. Make that: They detest each other.

The two own side-by-side breakfast nooks in Somerville’s burgeoning Ball Square, and their rivalry — of food and vitriol — is the stuff of neighborhood lore.

Separated by only a wall, Mirza, of Sound Bites Cafe, and Moccia, of the next-door Ball Square Cafe, have spent the past three years hurling insults and accusations at each other while serving up nearly identical menus of stuffed French toast, gourmet omelettes, and muffins. Restaurant inspectors, police, and the mayor’s office are all long-familiar with the feud. Even the Travel Channel heard of it and sought recently to capitalize on their animosity with a breakfast wars cook-off.

But now, the rivalry has come to blows. Outside their restaurants one recent afternoon, one attacked the other. Moccia said he punched his rival after Mirza spat on him. Mirza said Moccia beat him up for no reason. He has filed an assault complaint and hired a lawyer. Somerville officials, along with Ball Square business leaders, are desperately seeking ways to repair the relationship.

“It’s so sad that this has degenerated to the Hatfields and the McCoys and the Civil War,’’ said Jack Connolly, a longtime Somerville alderman who has frequented both establishments and knows both men.

The feud dates at least to 2007, when there was no Ball Square Cafe and Mirza, a Syrian immigrant, was doing a booming business with Sound Bites. At the time, his restaurant was in the space now occupied by Ball Square Cafe, and Mirza rented from landlords who happened to be Moccia’s parents. Facing a rent increase, Mirza says, he was forced to move. He bought the space next door and started over.

Moccia, meanwhile, had been working at the nearby Victor’s Deli, also owned by his parents. He says he had been looking for a change. And shortly after Mirza moved out, Moccia opened his restaurant in the space. He lured away Mirza’s prized chef, Omar Djebbouri, made him a business partner, and began serving breakfast, putting on the menu a number of Mirza’s offerings.

“I was inspired by Yasser,’’ Moccia said. “He had a great business. I just saw how hot breakfast was, and it seemed like it was the thing to do.’’

Both men, by all accounts, do a land-office business, attracting crowds that line up outside both restaurants, and Mirza says his continuing success has irked Moccia.

“He doesn’t like that I’m successful,’’ said Mirza, “even though he took my cook and stole my menu.’’