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Since the distribution is the same and the overall equity is the same, my first impression is that the variance will actually be the same for all of these situations. That is, a coin flip is a coin flip, no matter how complicated the "coin" is. In all cases, we have a sample size of a single hand, which we will win or lose, where we have 50% equity. There is no difference.

What am I missing?

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say our equity vs. his range is 50%. however say we both have the same hand w/ no redraws. our equity is and always is regardless of what card comes, 50%. this means no variance since we're always chopping the pot. if his hand range includes two hands one w/ 0% and one w/ 100% there will be variance because the results are different.