This old adage still exists today - “train where you plan to fly”.
That sounds more like old marketing rubbish.
British pilots have been undergoing flying training outside Europe since at least WWII—under the Arnold Scheme at seven British Flying Training Schools in the United States (
history), and across the Empire and Commonwealth under the British Commonwealth Air Training Plan. The former British-owned CTC and OAT had no trouble carrying on this tradition for civilian training outside Europe.
When comparing Canadian and British (EASA) private pilot training syllabuses the differences are far and few between which isn't surprising because both emerged from Smith-Barry's Gosport system. In some areas the overseas training is superior as for instance the spin recovery training and five hours of flight by reference to the instruments under the Canadian private pilot syllabus. Any differences in air law, air traffic services, and airspace can be learned by the average person in a week.
plus when you come back to convert everything...
In the context of this thread there is nothing to convert because any ICAO Annex I-compliant PPL(A) meets the pre-requisites for a Part-FCL CPL(A).
... you have to dump a lot of what you learned over there in the theory side.
That is of course a gross exaggeration and it overshadows the benefits derived from a diversified training experience. That is, there is a lot of theory taught "over there" which will be retained. There is a lifetime of learning in this business and in the end it makes little difference where one begins.