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The only way to make this close to a fair fight is to make them smart for zombies, but stupid for normal humans — IQs no higher than 50. So yeah, being able to open doors, use small firearms, follow simple commands, know how to hide for an attack, count to ten, and understand cause/effect; but nothing more complex than that. No "planning", really.
Essentially, they become the Velociraptors from Jurassic Park, only with opposable thumbs. Yes, as a human you're much more clever than they are, but they're also smarter than you THINK THEY ARE. If you consider them to be as dull as a post, you're gonna get eaten. If you think a mere door can stand in their way, you're gonna get eaten. If you think the one in front of you is the only one to worry about (another attacks from the side!), you're gonna get eaten.
As for the progression, it would be best explored (at least in the course of a novel, by my thought process) as going very slowly. I can see a normal person, once bitten, slowly and agonizingly having his mental faculties fail him (a la Flowers for Algernon) and being replaced by uncontrollable desires to consume the brains of increasingly complex creatures. At first, tearing into the brain of a sheep bought at a store, not even bothering to cook it, will sate you. A few days later, you beat your family dog to death and carve the brain right out of its smashed skull. Near as you can reason, this is a perfectly reasonable thing to do. There is no "right" or "wrong" left in your mind about killing a mere dog; there is only hunger. By the time you might have considered suicide to prevent the further tide of darkness, your morality has evaporated, and you go to your next door neighbor's house in the middle of the night and slaughter him and his family. Their brains are delicious, and nothing else seems to matter.
Deep inside, however, you still regret it, though don't understand why. Luckily, down the street is a loose commune of "people" just like you, and for some reason you don't have any desires to kill THEM and eat their brains. Perhaps, if you stayed with these people, everything would be okay; you wouldn't have that uncontrollable drive to murder anymore.
Unfortunately, a week later, a bunch of normals decide to attack your peaceful group. When they arrive, the urges come again, and once more you find yourself needing to kill again... to get inside their heads, and consume...