Whether the equipment was provided by the British as it was during World War I, or by the Canadian military as it was during World War II, the difference was technological rather than practical.
Canadians did have equipment produced in Canada for the First World War but it did not stand up well during training in England. So the soldiers inherited British uniforms and equipment.
Second World War equipment produced in Canada was sturdier ; however, there were still similarities between the equipment and uniforms of the two nations.