All told, nobody is quite sure which day is holier, Shabbat or Yom Kippur. On the one hand it seems Yom Kippur is holier because the Torah refers to it as “Shabbat Shabbaton,” the Sabbath of all Sabbaths. On the other hand, perhaps Shabbat is holier because God sanctifies it, whereas bet din, the Jewish court of law, sanctifies Yom Kippur.
This uncertainty has practical ramifications. Which of the following two prayers does one recite first on Shabbat/Yom Kippur – the Shehecheyanu blessing that celebrates Yom Kippur because Yom Kippur is the holier event, or the Shabbat Psalm of Mizmor Shir Leyom HaShabbat? No one is quite sure. Ashkenazi Jews recite Shehecheyanu first but Sephardi Jews recite the psalm for Shabbat first.
What everybody is sure about, however, is that the confluence of Shabbat and Yom Kippur creates the holiest day. First, Shabbat enhances teshuvah on Yom Kippur because the very word Shabbat includes the principal letters of teshuvah, taf, shin and bet. Second, the most powerful way to serve God is with joy, and Shabbat is a day of joy. Third, the synthesis of Shabbat and Yom Kippur reunites the two sets of the tablets of law, the first that was given on Shabbat and then smashed and the second that was given on Yom Kippur.
The blessing that is made over the Shabbat/Yom Kippur lights, which mentions both Shabbat and Yom Kippur is so powerful that it is no wonder we are lit up on this unique day.
And if one needed any more convincing of the rarified quality of Shabbat/Yom Kippur, we find it in the Havdalah ceremony. Whereas on a regular Yom Kippur we use no besamim for Havdalah, on Shabbat/Yom Kippur we do. That is because we take leave of the special Shabbat guest, the neshamah yeterah.