Competing was a win-win for EADS.
If they stayed out, Boeing would have a more profitable, less risky deal that would carry part of its manufacturing overhead.
If they won, they had a low-risk profitable deal.
Even losing, they have almost certainly forced Boeing to reduce its price and carry more risk, and may have pushed Boeing into something that will cost them a lot of money and further downgrade their reputation. However, losing doesn't make EADS look too bad, because most of the world assumes the fix was in.
The key was that the tanker was a must-win to Boeing, not so much to EADS. Strategically that is a bad place to get caught in.