Glacier has moose, bear (black and grizzly), deer, sheep, and goats that you stand a decent chance of photographing if you are in the right place at the right time. As far as roads and overall area you might see photographable wildlife, Glacier is considerably smaller. It's landscape is rugged and mostly timbered. What isn't timbered is either high elevation or very rocky.
Yellowstone has bison, elk, pronghorn, wolves, coyotes, foxes, sheep, moose, and bear (black and grizzly). Yellowstone has more area, much of it open or semi-open. Glacier doesn't take long to drive through, Yellowstone has more miles of road, by far, and more place to park and get out. Yellowstone gets to be like a people zoo in the busy season. My list of animals isn't complete, but only the major ones.
For a while after Yellowstone opens, and toward the end of the season, there are less people by a significant amount. In the spring the antlered animals like elk, deer, and moose will be in the process of growing new antlers. About the end of August is when they harden up and the velvet comes off.
As mentioned, Teton National Park is another option. Another would be a combination of the National Bison Range (not far from Glacier) and Glacier.
Keep in mind that there is no guarantee at all you will see some of the wildlife in these places, at least without spending a good amount of time trying. Bison are generally easy in YNP and the National Bison Range. Mountain goats are usually a sure bet in Glacier at certain times of the year. I would suggest that you start searching Flickr or the web for pictures taken in these various parks so you can see the typical wildlife shots and landscape. Different times of year and different areas with offer the potential for specific types of photos and scenery. If you have preferences, choose accordingly.
One week would be enough time to get a sample of all these parks and the National Bison Range, but you would be rushed and basically driving the whole time.