Between the two miracles of Chanukah (the oil and the victory), the more important one is unquestionably the victory. This is evidenced by the fact that it is the one we give thanks for. That is the one we couldn't live without. The miracle of the oil isn't that miraculous. There are many, far more miraculous events in our history without a holiday. The oil miracle is more an idea (hence, we study it). But, what is that idea?
The common answer is that it represents the battle between physicality and spirituality The Greeks were all about materialism and the physical while the Jews were all about the spiritual. The Greeks tried to rob us of our spirituality and convert us to materialism and physicality. The miracle of the oil demonstrates the laws of nature and the material world being broken to show the dominance of spirituality. A perfect message for life in exile. Torah=spirituality, the world=physicality. Torah > world.
That is why the miracle of oil became so central in the exile.
But, the truth is that the miracle of the oil was secondary. We don't even mention it in על הניסים. The battle was about our obligation and right to live a physical life infused by spirituality and holiness. That's why the decrees were ones involving action: don't circumcise, don't rest on Shabbat, don't purify in a Mikve etc… all of which represent the holiness of the physical.
The Greeks saw the physical and spiritual as separate and contradictory. Chanukah comes to show that they are not inherently separate, rather are both vessels for a deeper meaning and purpose – holiness.
That is what the miracle of the oil demonstrates and the victory miracle embodies – the ability of the physical to be "stretched" and hold more than just physicality; that the physical is a vessel for more.