Right now we don't compete with Emirates (which is fortunate for us.) This is due to geography. The only US markets they tap are US-eastern Africa and US-Indian sub-continent. They are a much bigger threat to the European legacies.
If cabotage rules change and they can start flying US-Europe we are in big trouble. You can't compete with their cost structure or level of service. Of course, extreme cabotage changes would allow Ryanair to fly within the US, at which point this career will officially by flushed.
^^^^^^^^^This hear is the bigger issue! It could happen.