As I am slowly adjusting to metric measurements in normal life I have also reflected several times on what are some ways to think about the differences.
Most simply, in my mind, its the difference between circular and linear.
Most imperial measurements are based on parts of a whole, e.g.: pie, circles, a group and fractions thereof. If you get circles - everything falls into place regarding much of imperial. It also allows for a different kind of precision (stuff that .33333, and .666666 just does not do). You will note that in measuring time is where we overlap circular measurement (parts of the whole of the year solar or lunar) and linear as the days and years pass.
Metric is all about linear thinking by 10s. It is more easily scaled because it flattens everything - except where it doesn't. Metric is a joyful discovery for a grade-school math student.
Now both systems have to compensate for their natural strengths and weaknesses when measuring different aspects of something. e.g. Metric shines in straightforward linear measurements. Imperial does well on the curve.So this thanksgiving I will probably eat 1/6th of a pumpkin pie - just don't try to cut me 0.166666666666666666666666666666666666666666 of a piece.