Which is better: Fasting the six days of Shawwal or making up the Ramadan days one missed due to a legitimate excuse?

The intention (niyyah) for obligatory fasting is specified by the Malikis and Shafi'is, and is one narration among the Hanbalis, which is the most preferred opinion based on the hadith: "Actions are but by intentions." The meaning of specification is to intend the fast to be for Ramadan, or its make-up (qada'), or expiation (kaffarah), or a vow (nadhr). Based on this, your fast will not be counted as a make-up for Ramadan; rather, it is a fast of the six days of Shawwal. It is permissible to observe the six days of Shawwal before making up for Ramadan, although it is better to prioritize the make-up fast.