It's hard to say really. Both are lovely.
Jasper has the amazing Lake Louise and the gondola up the mountain. The hike to the peak is steep, but smooth and well marked.
Even if you don't go higher than the gondola level, the views are spectacular.
The Icefields parkway is a nice drive and there are lots of viewpoints and short walks.
If you are interested in geology, Banff is close to the Burgess Shale, which is one of the largest fossil beds in the world.
There are interpretive geo-walks and so forth available too.
Drumheller is about 3 1/2 hours from Banff, so if you want world class dinosaurs, it's very accessible. The drive down into the badlands is quite striking - the area goes from flat / gentle foothills and then the badlands appear like a slice through the prairie. In late summer it will be hot, but beautiful.
I guess it really depends on what you want to see and do.
Art? History? Geology? Nature? Fishing? Hiking? Fine dining? (Banff has a famous wild game fondue restaurant.)