I switched from Koodo to Telus using the same phone (Samsung Galaxy Core LTE). The signal is harder to catch, I have a lots of trouble getting a line or sending/receiving a SMS.
Is there any special procedure that I should do beside inserting the new SIM card?
I thought about re-initialize the whole thing, but that would erase all my contacts and music.
No, no special procedure. Since the towers are the same, there should be no difference in reception. I take it you turned the phone off to swap the SIM?