The Parsha most closely associated with Purim is Terumah and the one most associated with Chanukah is Behaloscha.
The names of both Parshas refer to the ways in which we ascend when we aspire and contribute.
Terumah comes from Rom. The portion that is separated is raised up as a contribution to G-d. Behaloscha likewise refers to an ascending, whether it is that of the priest rising to light the menorah or the light of the oil flame which, Rashi tells us, must be lit until the flame rises on its own.
The Terumah is collected from Ish Asher Idvenu Libo, the man whose heart is moved to contribute to the construction of the Mishkan. The flame of the menorah too is only properly lit when it rises on its own. The temples of G-d are best built with offerings that are freely and joyfully given.
The list of the offerings appear linear in value. Gold, silver and copper. This runs from the most precious to the less precious. The pattern continues with various fabrics dyed in colors. Turquoise, purple and red. Purple was the color of Roman royalty because of its great value. Red was used by the Redcoats because the wealth implied in red dye demonstrated power. Yet the most precious dye listed is turquoise which represents heaven. Only on the ark does the turquoise dyed cloth appear on the outside rather than under the hides. This listing then goes on to wood, the least precious of these.
But then it lists spices, oil and the precious stones used for the Kohen Gadol, the High Priest. Are these truly less valuable than wood? In pure material worth, they are more precious. But what these items, the Shoham stones, the oil, spices, incense and precious stones have in common, is that they were donated by the leaders of the tribes.
In Parshas Vayakhel, Nesiim is spelled defectively because, we are told, the tribal leaders waited to give. They intended to see what would be missing from the donations and fill it in. And so their donations mattered less for the delay. It is not the mere material worth of the item that makes it precious, but the enthusiasm and love of the donor.
In Behaloscha, Rashi inquires why the previous parsha which lists the offerings of the nesiim is linked to the menorah lighting. The answer is that Aaron felt bad that all the tribal leaders had provided lavish offerings, with which they had compensated for their previous tardiness, but he had been left out. And thus G-d told him, Shelecha Gedolah Miselachem, yours is greater than theirs.
Aaron's act of kindling the menorah, of lighting the flame so that it rose, was greater than their offerings. Furthermore his descendants, the Maccabees, would redeem the temple in Chanukah by fighting for its liberation against a corrupted leadership that had collaborated with the Syrian-Greek tyrant. It was not mere wealth that mattered, but the flame and enthusiasm of passion.
In Terumah, material donations are needed to create the items of the Mishkan, the Tabernacle. But the actual dwelling place for G-d, is not built out of mere material, but out of our love and enthusiasm.
Purim likewise represents a material struggle against a material evil. The name of G-d is not even mentioned in Megilat Esther. But outside the picture were the small number of Jews who had returned from exile and were struggling to build the temple. The drama in the court of the king was ultimately about that rebuilding of the temple.
It is in Chanukah that the rebuilt temple is defiled and menaced. The war is not physical anymore, but more deeply spiritual. It culminates in the lighting of the menorah and the miracle of the oil. But the memorah that is lit, according to some opinions, is not the solid gold one of the temple. The menorah of the temple had been defiled. Instead a menorah of wood was temporarily used. Though it was made of the lowest material on the list, it served the highest purpose.
Material matters cannot and should not be disregarded. But neither are they all that matters. Material progress must culminate in spiritual achievement. The material becomes meaningless when it can no longer act as a metaphor and a vehicle for the spiritual. A wooden menorah that is kindled for G-d is better than a defiled golden menorah.
The gifts of the tribal leaders, precious as they were, mattered less than the humble wood donated immediately as an outpouring of devotion, and as the sacrifices of Aaron and his descendants.
Both Purim and Chanukah are holidays of the exile. Purim is a holiday of the day. Its primary mitzvahs are performed in the daylight hours. Its materialism is simple. G-d is hidden in the megillah. Its holiness comes in the challenge of finding G-d in prosperity, in celebration, in feasting and drinking, in the seeming triumph and the happy ending. Chanukah is a holiday of the night. Its most significant celebration is in the evening. Its physical victory is extremely fleeting. Its spiritual victory is the one that matters. In the darkness, light is all the more visible and even when G-d is absent, we can more clearly see Him. And thus it is Chanukah, not Purim, which has the most obvious miracle.
But the significance of both lies in the power of our aspirations to raise us up to G-d.
Mordechai's speech to Esther, answering her seemingly sensible objection and call to delay with warnings that salvation would come from elsewhere and her father's house would perish if she did not take action, seems irrational. And yet that is the significance of both Chanukah and Purim.
G-d will eventually always save us. He does not need us to act. Nor does He need us to build Him a home. Or to light a lamp for Him. The significance of such actions is not that they help Him, it is that in doing so we save ourselves by elevating ourselves.
In exile, G-d often appears distant. By reaching toward Him, we transcend ourselves.