The contrast between על הניסים and the gemara's account
When we look at על הניסים we see that it focuses exclusively on the נס of the war. It doesn't mention the נס of the candles whatsoever. The gemara in Shabbos however, focuses almost exclusively on the נס of the candles while neglecting the war. What is going on?
The Maharal asks how can we say hallel for the נס of the candles? Hallel is to thank Hashem for saving us, the נס of the candles was not in that category. He answers that really we say Hallel for the נס of the war.
The Pnei Yehoshua asks why was the נס of the candles needed after all, טומאה הותרה בציבור and they were all טמא? The answer is that you are right, the נס was not needed, it was a נס of לכתחילה.
With this we can understand our original question. על הניסים is part of the הודאה section of shemno esrei. There we thank hashem. Therefore we talk about the נס of the war. The נס of the candles has no place there it is not something that we need to thank hashem for. The gemara however, has a different focus. The gemara is trying to get us to focus on the yad hashem. The נס of the war was a hidden נס. It was done in a natural way. Chazal were afraid that if they focused on the נס of the war people would forget the yad hashem and think כחי ועוצם ידי (we can understand this well, just look after the 6 day war). They viewed the fact that hashem made a נס of לכתחילה as supporting this position. The נס of the candles was not needed so chazal understood that it was there to teach us something else. Namely, that just like the נס of the candles was a נס, so too the victory of the war was a נס. Therefore Chazal placed an emphasis on the נס of the candles so that we would understand that the war was a נס as well and not lose focus and fall into the trap of כחי ועוצם ידי about the war.