Short answer: it depends. lol, I bet that clears it right up for ya!
GI has to do with much more than just the type of grain, although that's involved. Wheat is lower GI than rice, but higher than say, quinoa (not that you're likely to find quinoa bread). So if a bread is really 100% whole grain, it may be slightly lower GI depending on the grains (though I doubt it would have any actual impact on body comp - not a significant enough difference).
The more finely ground the flour, the more surface area each particle has, and the higher the GI. You can have two kinds of whole wheat bread with identical ingredients except for the processing of the flour, and the one with stone ground flour will be lower GI than the one with machine processed, very fine flour (such as you might find in a 100% whole wheat bread by Wonder or some other very processed, cheap type of bread).
Additionally, most 'whole grain' breads do actually contain white flour, so read ingredients carefully.
Finally, other ingredients make a huge difference to GI. Does the bread contain sugar? Higher GI. Does it contain sourdough starter? Lower GI.
Also remember than eating bread with a little protein, fat and especially vinegar will lower the GI. Try mixing a little extra-virgin olive oil, red wine vinegar, cottage cheese and pepper. Yummy.
Hope this helps!