FWIW, my understanding is Rogers doesn't support something called fast dormancy (very long explanation short: if the phone is connected for data but idle, the connection is depreciated from 4G down to eventually 1X - this minimizes the phone's impact on the carrier and reduces battery demand; start to move data and the connection ramps back up again - all of this is done very quickly). The good news is there's an app to disable the phone's attempts to use fast dormancy. But... the phone must be rooted to use the app.
I ran into the fast dormancy issue in the Bahamas (Bahamas Telephone Co.). Using their SIM in a RAZR MAXX, the phone would basically become slower and slower until it locked up. Reboot and the process started all over again. Voice-only worked 100%. Cutting to the chase, the problem turned out to be fast dormancy isn't supported by BaTelCo. The fix for the RAZR MAXX was to root the phone and edit a system file called build.prop (there's an app for that - the needed code can be found with Google). In doing the research on this problem, Rogers came up as also not supporting fast dormancy. All of this happened two years ago, so things may have changed. I haven't been back to the Bahamas since then and I've never used Rogers. NTL, I'd take a serious run at getting the answer to this question. It may take some pushing but Rogers should produce the answer sooner or later.
Summarizing, AFAIK your VZW S5 should be just fine in Canada. My guess is fast dormancy is the key to why 4G may not work. And there is a work-around for that.
All of that said, please remember I do not have first-hand experience with my VZW S5 in Canada or anywhere but the US. I'll return to the Bahamas a few months and be in Germany in December; I expect to know much more then. But I doubt you want to wait that long for my first-hand report.
A winner is a loser who tried one more time.