Okay, so your chilluk isn’t so much between more specific vs. less specific tefillos, but more between a period of relative calm vs. a time of more acute danger. It did not appear this way from your third post on this thread.
So I will again highlight a chilluk which I made: the chilluk between feeling hakaras hatov and expressing it. Normally, the feeling of hakaras hatov should be expressed, but in the specific case of the Medina and Tzahal, many feel that the inyan of expressing (as opposed to feeling) hakaras hatov, particularly in certain ways, is counterbalanced by strong hashkafic considerations.