The Tetons have several classic places to photograph. Some of these include:

Mormon Row
Schwabacher's Landing
Snake River Overlook

There are also a great number of places that you can go to do hiking. Jenny Lake, for example is a great place to day hike. There are also many trail heads between Grand Teton and Jackson (such as the Death Canyon Trail Head). It has been my experience that moose are more abundant around the Tetons than in Yellowstone (though they are abundant in the Park as well).

To me, when you talk about Yellowstone, you mean 'wildlife' though there are great landscape opportunities as well. For example, the hotpools are a treat, particularly on a nice overcast day so the colors get nice and saturated. I find the Lake Region, off by Sylvan Pass, to be very beautiful. Going up towards Mammoth also yields many opportunities.

James

PS As I write this, I keep thinking of all the many places there are to photograph. There are almost too many, which is why after over 10 trips to Yellowstone that I am still enchanted with the place.