As far as down and across versus over up over up – exactly the same distance assuming a perfect grid.
Not accounting for any time you’re NOT walking (Such as waiting at a street corner which may or may not be predictable), whatever gives you the shortest distance. e.g. the closest to a straight line as is possible is fastest. So if there’s for example, a park you can cut through diagonally that will save you time. Given a perfect grid with none of these opportunities – doesn’t matter.
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