According to the Tzemah Tzedek, the third Lubavitcher Rebbe, in his book Derech Mitzwotecha explaining about the mitzwah of Hannukah candles, the light that is revealed on Hannukah and Purim is so powerful and from such a high place that we cannot readily receive it.
We awaken the revelation of the light with the performance of the mitzwah, but the light itself is beyond us. Since it is beyond us, we can't mistakenly transmit it to the dark side, to the elements of creation that utterly lack holiness.
By contrast, on Shabbath (and Yom Tov) the light brought down is specifically meant to be received, and when we create (through our mitzwah observance) the appropriate vessels we do receive enlightenment. It is for this reason that we don't do melachah, we don't involve ourselves with anything lacking inherent holiness. If we were to be involved in the mundane with such a level of enlightenment, then we would be channeling all of this divine influx directly to the unholy forces, the dark side. For this reason (among others) HaShem commanded us to abstain from worldly concerns on Shabbat and Yom Tov.
On Hannukah, where we ourselves cannot receive this tremendous light, there's no need to abstain from worldly matters, there's no danger of us transmitting any of the divine illumination to the other side.
There are two areas of specific interest to women on Hannukah:
- A wife who lights the Hannukah candles in the home completes the mitzwah for her husband--even against his will. This means that if the husband is away from home and he intends to light the candles himself, purposely intending not to be included in the lighting his wife will perform in the home, he is still included in her lighting, and has no need or mitzwah to light the candles himself. To me this is interesting because there aren't many mitzwoth at all that can be fulfilled for someone in direct contradiction to their own intent or desire, completely against their will. The reason in our case is because the mitzwah rests primarily on the home, not on the individual (wherever they might be) and women and men are both obligated to light Hannukah candles.
- While there is no mitzwah not to perform melachah as we mentioned already, there is a custom (and Jewish customs are like Torah) for women to abstain from melachah during the half hour or so that the candles are supposed to be lit. I wanted to suggest that this implies that even though, in general, the light of Hannukah is beyond our perception, women are able to attain a certain level of connection with this light, and consequently they aren't supposed to work during the time of candle lighting.