I have never heard either of these possible approaches referred to as American or European. Here in the states every institution has it's own preferred method of treatment, and many use both that you have suggested depending on many factors including the patients ability to tolerate various treatments, the staging of the cancer, and preferences of the treating professionals. They are essentially the same treatments except for the order in which they occur. As to one possibly eliminating surgery, I think you will find that the consensus of opinions favors a neck dissection regardless of what the final result