Obvious example is We Will Bury You vs. Duck and Cover. Whoever plays Duck and Cover will lose in that situation, as it has the lower Ops value and goes second.
Of course Defcon has to be 3 for that example.
Another example at Defcon 3 is Duck and Cover and Olympic Games.
An example at any Defcon is How I Learned to Stop Worrying (USA) and Olympic Games (USSR).