The difference between replicated food and non? I'd say that there isn't one - but people BELIEVE there is a difference. It's like the same meal being made by two different people. The food can be made exactly the same way with the same ingredients, but people will percieve a difference. In the case of 'home-cooked' versus 'replicated,' there's the human desire for that 'human touch.' It's why hand-crafted items still have a heavy market, even though you can buy a mass-produced item that does the exact same thing.
But I don't understand one thing - where does this idea that there's replicator 'hate'? The characters all ate at the Replimat (Which, by the first three letters, I would assume relied heavily on the replicators). The characters ate at Quark's, and, let's face it, there's no way in hell that Quark would spring for the expenses of getting the actual food shipped out OR having to pay employees for food prep. In those cases, clearly, the characters are going to those places less for the food and more for the atmosphere.
Is it because Sisko was always making his own meals? Well, remember, the man's father owns a restaurant, so he grew up making these meals.