Hanukkah candle and Shabbat candle

If you're already entering into obligations that are outside of halakhic law, then there's no need for all this. Just say that halakhic importance doesn't necessarily reflect essential importance. Beyond that, you are essentially saying that these two statements do not contradict each other because they do not deal with the same situation: in principle, a Hanukkah candle is preferable to the mitzvah of a Shabbat candle, but a Shabbat candle itself (not the mitzvah) is preferable to a Hanukkah candle. It seems to me that the simple interpretation is that it is indeed a non-transitive relationship (there are others in the halacha). For example, the loss of a father and the honor of his father (Tos. P. B. D.M.) and so on. That is, when he has ten shekels and has the option of buying either a candle for Chanukah or a candle for Shabbat with them, he should buy one for Shabbat. When he has a Shabbat candle and does not have a Chanukah candle, he should sell everything he has in order to buy one. And when he does not have a Shabbat candle, he is not obligated to sell everything he has in order to buy one. According to this, in the situation you described, after he sold his blanket, he must use it to buy a Shabbat candle and not a Hanukkah candle. Because after selling, he has money for one of them, and in this case a Shabbat candle is preferable. It is true that the explanation for this should be discussed. It seems that there are different axes of priority here: the normal needs of one's household are preferable to a Shabbat candle, but not preferable to a Hanukkah candle. But a Shabbat candle is preferable to a Hanukkah candle.