In the urban areas of the state, not much if any difference in the small group of carriers. In between the urban areas, cell service with any of them is very spotty or non-existent. Some locations, I have found a good signal in strange places, such as close to some of the Alaska Oil Pipeline pump stations. Suspect Homeland Security or the oil company paid for a tower somewhere in the area. But for the most part, service between urban areas is zilch, nada, kaput, etc.
I have AT&T for cell service with a data plan with my iPhone and iPad and then have a Verizon data plan for my MiFi device. The last trip, I didn't activate the MiFi plan, a pay as you go one, as I was able to use AT&T everywhere I needed it. One of the state cell carriers put cell service into all the villages in Alaska, but not sure if they are on the same frequency as my phone. Driving by some of the villages, over by Northway, Tok, etc. I have never been able to pick up their signal.
I have a good friend that works for the Alaska Railroad on track maintenance and he carries two cell phones, plus his portable railroad issued two way radio. He claims he can call into the Anchorage office, most places from Fairbanks to Seward, with one of the three devices. Verizon is fairly new to the Alaska market, and were renting tower space from someone else. Latest I have heard is they now have a presence in the state, but whether or not they are installing their own towers or not, I don't know.
With the limited population of Alaska, it is doubtful if the cell coverage will ever get "good", until cell phones can start using satellites, instead of fixed towers. Service is better, if you have good, line of sight, such as driving south of Anchorage, headed for the Kenai. I get a good signal down to about the Hope turnoff, because the signal from the Anchorage tower is passing over Cook Inlet and no mountains or trees to interfere with the signal.
Check with your carrier before using a cell phone or data in Canada, as it can be very expensive. Same applies for Canadians in the US. You can get hit with both roaming and long distance charges if not careful.