Bison bonasus. They eat a lot of trees. Image from Michael Gäbler, Wikimedia.
The diets of grazers and browsers have not been easy to determine. To determine the diets of animals you have to 1) spend a lot of time watching, 2) use exclosures, 3) grab the food somewhere in the digestive system and try to recognize it. None of these approaches work that well.
Recently Kowalczyk and others published a paper that sequenced plant DNA present in fecal material from Bison bonasus in Bialowieza Forest in Poland. Essentially, a lot of plant DNA makes it through the digestive tract and it can be sequenced to quantitatively assess diet. This all but renders options 1, 2, and 3 vestigial. My guess is that we are going to see a lot of this technique in the near future. It's too powerful and the results are too fascinating.
Right now it costs about $12K to run 96 fecal samples with 454 sequencing. $12K is a lot, but $100 a sample is not.
The specifics of what the authors learned from the technique is interesting. Bison bonasus diet consists of a lot of trees and herbs. And the tree species are not economically important, which makes them great forest gardeners. Compared to Bison bison, Bison bonasus might as well be Alces alces.
Kowalczyk, R., P. Taberlet, E. Coissac, A. Valentini, C. Miquel, T. Kamiński, and J. M. Wójcik. in press. Influence of management practices on large herbivore diet—Case of European bison in Białowieża Primeval Forest (Poland). Forest Ecology and Management.