I've technically been to both areas, but don't count my time in Alaska as a real outdoors trip (did a cruise in the Inside Passage). Based on what I've read and what others have said, I think if you're looking for accessible day hiking, the Canadian Rockies might be a better choice.
We've been to the Rockies twice and love it there. Generally, Banff is better for dayhiking than Jasper. I would check out some of the other parks too. Yoho has some really nice dayhiking (beware though if you want to go to Lake Ohara -- it takes some jumping through hoops). We didn't dayhike in Mt. Robson or Kootenay (did backpacking), but I imagine there would be some nice day hikes and at least for Kootenay, they only get a fraction of the visitors the other parks see.
The best book I've seen for Canadian Rockies is
The Canadian Rockies Trail Guide by Patton and Robinson. Very useful for planning a trip.
The dayhikes we've done are Lake Helen/Cirque Peak (Banff), Fairview Mountain/Lake Louise (Banff), Sentinel Pass/Eiffel Lakes (Banff, me), Sentinel Pass/Mt Temple (Banff, Steve), Burgess Pass (Yoho), Iceline Trail (Yoho).
FYI, our pictures/notes from both trips are here (2006 is probably more interesting because we were there longer and had better weather):
Canadian Rockies 2005
Canadian Rockies 2006
ETA: a few other things ...
Rockies are super busy in August, less so in September, especially after Labor Day. If going in August, you will probably want to plan accomodations further in advance.
We found that people don't seem to get up to early in the Canadian Rockies. Hitting the trail by 8 (which to us is on the later side) in nearly every instance provided for solace at the summits.
If you are used to hiking in the NE, I think you will find the hiking in the Rockies easier (switchbacks, easy grades, nicely maintained, etc). Just to keep in mind when looking at mileage for hikes.
Some trails in Banff have a minimum group size requirement of six due to grizzly activity. The first year we went some of the trails in Jasper were closed for the same reason.