You can use the DiffCommand by creating AbstractTreeIterator instaces for the branches and then use the DiffCommand to return you a list of differences between the two branches:
// the diff works on TreeIterators, we prepare two for the two branches
AbstractTreeIterator oldTreeParser = prepareTreeParser(repository, "refs/heads/oldbranch");
AbstractTreeIterator newTreeParser = prepareTreeParser(repository, "refs/heads/master");
// then the procelain diff-command returns a list of diff entries
List<DiffEntry> diff = new Git(repository).diff().setOldTree(oldTreeParser).setNewTree(newTreeParser).call();
for(DiffEntry entry : diff) {
System.out.println("Entry: " + entry);
}
The full example including creating the AbstractTreeIterator can now be found as part of my jgit-cookbook