Neither system is more logical. They are just different. Metric is easier to use.
More accurate? That may have a practical explanation. Designs and drawings using inches commonly use three decimal places or, in other words, thousandths of an inch. Designs and drawings using mm commonly use two decimal places or hundredths of a mm.
A hundredth of a mm translates to 0.000393... inches which is about 2/5ths of a thousandth of an inch.
So using the most common precision that is in common use for each of the two systems of measure, the metric design/drawing will be expressing the dimensions with about 2.5 times the accuracy of the one using inches.
Or at least apparently so at first examination. Yes, the tolerances are always a part of a mechanical design/drawing. And they should ALWAYS be expressed in any drawing. But metric does encourage/suggest the use of greater accuracy in the design process. Drawings of electronic parts where the tolerance is not expressed, 1.23mm is a more precise dimension than 0.048" because in each case a +/- one count in the last digit is assumed. And 0.01mm is less than 0.001" = 0.0254mm.
While this is not the way drawings using each system should be looked at, it is the way that some, dare I say many will look at them.
My two biggest frustrations are:
1) People who claim metric for dimensions is more logical; and
Metric is more logical, for the simple reason that every scale is related by powers of ten, whereas we have 12 inches to a foot, 3 feet to a yard, 1760 yards to a mile, etc. However, there is no advantage in using metric for PCB design because that uses decimal inches (eg 1.27 inches). No feet and yards there.
2) People who thing metric is more accurate.
Really? I've never heard of that before. Does anyone really think that? I wonder if they mean more precise rather than more accurate, but of course that is nonsense, too. You can dial in any level of precision you want with either system.