It's a gamble either way, since you can't predict which way the exchange rate will move over the next three years, nor the interest rates in each country.
By transferring the money at regular intervals, you get an exchange rate which averages out, whichever way it changes. If you transfer at the end of the stay, you get the exchange rate at that time, which could be better or worse than the average.
The exchange rate doesn't vary much by size of transaction if you use a third party exchange specialist like Currencyfair, or CurrencyOnline. Many Canadians use Custom House (now part of Western Union, also at xe.com) for their international exchange because the payment to them can be made (free) with bill-pay from many Canadian banks. The Custom House rates are not the very best available, but the lower transaction costs help.
I would generally go with a quarterly exchange, except for one thing: you might not want or need Euros at the end of your stay. You might want to stay in Canada, go to the US, go to Australia (it's warmer...), or somewhere else. You'd then have to convert the Euros onwards to another currency, rather than just from CAD.
A compromise, if the figures are large enough, is to transfer half of the savings at regular intervals via a low-cost route, and keep half in Canada. The half in Canada would be your starter funds for another country, or to change in into Euros at the end if that where is you decide to go.