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what effect does bullet diameter have on knockdown power, all other factors being equal.
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Knockdown power does not exist. It has been theorized by many gun writers and ballisticians, but no one has ever demonstrated that a bullet of larger diameter can "knock down" an animal. Possibly the fault of that pesky Newton guy and his laws. On the contrary, a smaller diameter bullet effectively transfers energy AND has better ballistic coefficient for a given weight. They seem to hit very hard also, possibly because to get a smaller diameter bullet to fly true you have to use a tighter twist, thereby increasing bullet upset upon impact. Roy Weatherby built a whole rifle empire on that basis.
Theoretically, larger diameter should provide a greater area of impact, but in reality there is little difference in effective frontal area with calibers typically used for game hunting on the North American continent. However, if you want to get extreme, a 4-bore rifle (1" bore diameter) will definitely let your game know you are serious.
Larger diameter bullets are usually heavier than smaller caliber projectiles. One thing that heavier bullets do well is penetrate through hard, tough, dense tissues like bone or heavy muscle, but few of us will ever need to test that because we primarily shoot thin-skinned, lightly muscled game on this continent, with the possible exception of large bears.