On the Friday night during Chanukah, the Chanukah candles are traditionally lit before the Shabbat candles. This is because once the Shabbat candles are lit, it is Shabbat, so lighting fire is forbidden.
However, I recently spoke with a minyan that started their Friday night services well after sundown, and had an optional candle lighting right before services for those who wanted to take part. This is certainly widespread. So the question is, in what order should Shabbat and Chanukah candles be lit if they are lit after sundown?
One who is lighting candles after sundown is implicitly holding that lighting fire on Shabbat is permitted. Therefore, it seems to me that the reasoning above does not apply, and the principle of "tadir ve-she-eino tadir, tadir kodeim" should predominate. This principle states that a more common action should precede a less common action. (This is why shacharit precedes musaf, and why (according to Beit Hillel, whom we follow) borei peri hagafen precedes mekadeish ha-shabbat in the kiddush.) Therefore, since Shabbat is more common than Chanukah, it seems to me that in this circumstance, Shabbat candles should be lit first.
UPDATE: I received the following response from a correspondent who wishes to remain anonymous. Which approach is correct? You decide.
Just read your posting about Hanukkah/Shabbat candles - apparently I'm not up-to-date enough to actually comment on the blog itself, but here's my take: you're wrong in saying that people who light after sunset are implicitly holding that kindling fire on Shabbat is permitted. In fact, I would be very surprised to hear anyone who does light at such a minyan say that. I bet instead they would simply say that they light candles for Shabbat and Hanukkah, and hence light them before services - in other words, they're not Shabbat-observant. I think it's nice to try to judge them in the most favorable light possible - which I think you're doing in trying to force their actions into a halachic framework - but in doing so I don't think you're fairly representing them.
On a more practical note, I would suggest two things, from a halachic point of view, since there is really no way in halachah to support lighting fire on Shabbat:
1) It would be better to light using electric candles, since there is ample halachic support for the notion that using electricity is permitted on Shabbat, even if observant communities do not actually do so. It would be best to use battery-powered lights, so that the "fuel" is limited just as it is with regular candles.
2) You should still light Hanukkah candles before Shabbat candles, for a few reasons - first, "lo plug." Just because in this case you are lighting after sunset should not cause you to think that in general you should light Hanukkah candles after Shabbat candles; second, "lo titgodedu": it is better to light candles the same way Jews around the world are. We have our many and varied differences, but is it necessary for this to be one too? I think not.