This is such a vast question because agriculture globally is highly variable and locally contingent. There is simply no way to generalize about differences between hemispheres in a meaningful way. About the best I can do at the moment is to recommend Giovanni Federico's recent survey of modern agriculture, Feeding the World. It is essentially an economic history, but it is environmentally informed and one of his central points is the great diversity of agricultural systems and practices around the world. He only covers from 1800 to 2000 though, so I'm not sure if that's what you're interested in. I don't know of anyone who surveys agriculture around the world before that.

One thing I will recommend is that you put down Diamond and pick up Alfred Crosby's Ecological Imperialism. The critiques of Diamond are many and sharp, and you can read them in the FAQ. The bottom line for me is that Diamond is not a historian and consequently he makes a series of problematic assumptions about the past: he does not understand historical specificity or complexity, he overgeneralizes, he assumes that certain principles are universal, and he WAY overextends his conclusions. In short, he doesn't know how much he doesn't know. Alfred Crosby, on the other hand, made some very similar arguments to Diamond, but he's a professional (and highly respected) historian. He understood the limits and pitfalls of the arguments he was making, he has a much better command of the source materials, and he's far more circumspect in his conclusions. Plus, he wrote his book 15 years before Diamond. Indeed, Guns, Germs, and Steel is basically a ham-fisted, amateur rip-off of Ecological Imperialism, the latter surpassing the former only in its marketing budget and the arrogance of the author. Plus, Ecological Imperialism has been around a long time, and you could find it on amazon for under $10, perhaps even under $5.