Either route will be fine in your rig, Waterton Lakes NP is the big attraction on the east side. From there north on 22 things are a little sparse till High River then your in heavy traffic from Calgary. Alberta 40 not good for your rig.
West side , from Whitefish 93 is the route that would be my choice, more parks , Fort Steele, Fairmont & Radium all have many parks to choose from , I'd stick with 93 from Radium through Kootenay NP. Always enjoy that drive.
JMHO: #1 the Trans Canada , is the major truck route, heavy traffic in summer, and staying on 93 puts you on #1 for the shortest time to get to Lake Louise.
EDIT: Monday Aug. 4th is a holiday in BC. and I think Alberta. Crossing the border even at a smaller port of entry may be a real hassle, due to volume . Tuesday for crossing would be better.
RE-edit , I always have second thoughts , particularly when my DW reminds me of stuff. On the Canadian side en-route to Fort Steele , there is a railroad , level crossing that's not so level, had my 5er airborne over that one.
99DSDP 3884, Freightliner, XC, CAT 3126B, 300 HP /ALLISON 3060
2000 Caravan toad, Remco & Blue Ox.