Tom,
According to theweathermetwork.com, the average high in both places is about the same...14 or 15 degrees (Celsius) in May, and 19 or 20 degrees in June. Comfortable weather, but Ian's right...at that time of year, you could get ANYTHING for weather! I was hiking years ago on the B.C.-Alberta border in mid-July, and we got 3 feet of snow overnight, and a week later Edmonton got flooded from all of the snowmelt out of the mountains.
Not sure it's possible for you, but I would highly recommend early-mid September instead...much nicer time of year to play. The courses would be in much better shape at that time of year. Nights are a bit chilly, but the days are gorgeous, with warm weather, and some beautiful scenery.
If you wanted to play at another course "in the area", I would strongly suggest "Stewart Creek", just south of the town of Canmore, which is just east of the Banff National Park east gate. It's about a 15-minute drive from Banff townsite. I played there last August, and it's a beautiful course, cleverly designed into the side of a mountain [and incorporating old mining features, such as shaft entrances, etc...in fact, one is visible in the top photo below...between the two fairway bunkers] by Gary Browning of Calgary, Alberta, who is also building another course for that area, which will become the new public course there and Stewart Creek will become private in another year or two.
A couple of pics are below, from last August...top photo is the view from the 1st tee, and the bottom photo is a bit later on the front nine.
JJ