It doesn't really make any difference for (avoirdupois) weights, but it does matter for liquid volumes, where the British fluid ounce is slightly smaller than the American fluid ounce, and the British gill has 5 fluid ounces versus the American gill of 4 fluid ounces. This propagates upwards through half-pint, pint, quart, half-gallon, gallon, etc., each having the British measure almost (but not quite) 5/4 of the American measure.
Mostly, this means that Canadian fuel prices are harder to relate to American fuel prices, and British pints of ale are bigger than expected.
Reading 1984, it took a little bit of thought to understand why the old-timer was complaining about only getting half-liters of beer rather than true pints.