Git offers a couple of great commands for comparing branches. To get a comparison of branches in a "status" type format:
git diff --name-status branch1..branch2
Will give you output something like:
M config/boot.rb M config/database.yml M config/deploy.rb M config/environment.rb M config/environments/development.rb M config/environments/production.rb M config/environments/staging.rb
Now that you have a list of files, you may wish to get a diff of a specific file:
git difftool branch1:config/environment.rb branch2:config/environment.rb
On OSX, this will open the awesome FileMerge.app allowing you to compare both files.