On Simchat Beit Hasho’eivah not all are equal: “Pious men and doers of good deeds would dance,” while the rest of the people would only come to watch and listen. On Shemini Atzeret and Simchat Torah, on the other hand, all the people-men, women, and children-rejoice.

The difference can be explained as follows: Simchat Beit Hasho’eivah is connected to a defined cause-the holiday of Sukkot and the water libation. Consequently not all are equal. However, the rejoicing of Shemini Atzeret and Simchat Torah is not tied to a specific mitzvah or a special concept; so rejoicing emerges as an independent theme. Therefore there is no limitation on who may participate.

More specifically, in each of the three holidays there is a specific cause for rejoicing, either the mitzvah of the day or the special theme of the day. The cause of the rejoicing on Pesach is that it is “the time of our freedom”; on Shavuot that it is “the time of the giving of our Torah”; and even on Sukkot, which is “the time of our rejoicing,” the rejoicing is tied to the mitzvah of the day, sukkah and lulav.

Therefore the rejoicing of Sukkot, stemming from the fulfillment of the mitzvah of the day, is limited according to the character and scope of the mitzvot; and just as all are not equal in the fulfillment of these mitzvot (a woman is exempt from them, etc.) similarly not all are equal in the measure of rejoicing.

(Likkutei Sichot, vol. 14, p. 166)