Rabbi Shimon Bar Yochai and Moshe Rabbeinu
The question is widely asked: Why is the 7th of Adar, the yartzeit of Moshe Rabbeinu, observed with a somewhat mourning flavor, while Lag Ba'omer, the yartzeit of Rabbi Shimon Bar Yochai, is observed as a day of celebration and festivities?
I saw a number of answers to this question in the "Kuntres Lag Ba'omer B'halacha U'vaggada" (compiled and self-published by Rabbi Shimon Gutman).
For one, Moshe Rabbeinu represents Torah shebektav, the "written" or "revealed" Torah, while Rabbi Shimon Bar Yochai represents the Torah she ba’al peh, the "oral" or "hidden" Torah. It is explained that according to kabbala, the yartzeits of tzaddikim who are associated with the written Torah should indeed have a mourning flavor to them, while the yartzeits of those associated with the oral and hidden Torah should be celebratory in nature.
Another answer is that Rabbi Shimon Bar Yochai specifically promised that he would advocate in Heaven on behalf of klal yisrael every year on his yartzeit, praying that we be saved from every trouble and woe. Since we are confident that Rabbi Shimon will be successful in his mission, it is a day worthy of celebration.
It is also important to note the difference between what occurred on the day that Moshe Rabbeinu died and what occurred on the day that Rabbi Shimon Bar Yochai died. When Moshe Rabbeinu died, three thousand halachot were forgotten from klal yisrael, making the anniversary of such an event worthy of mourning in its own right. When Rabbi Shimon bar Yochai died, however, three thousand halachot were revealed and renewed, making the anniversary of such an event worthy of celebration.
There are also a number of connections between Rabbi Shimon bar Yochai and Moshe Rabbeinu. For example, it has been suggested that the bonfires that are a feature of the Lag Ba'omer celebrations are intended to recall the burning bush. There is also the well-known teaching that Rabbi Shimon Bar Yochai was the reincarnation of Moshe Rabbeinu. According to this approach, Lag Ba'omer represents, to some extent, the fulfillment of Moshe Rabbeinu's longing to be buried in Eretz Yisrael! Indeed, many people visit the tomb of Rabbi Shimon bar Yochai on the yartzeit of Moshe Rabbeinu.
It is also noted that Lag Ba'omer is a day worthy of celebration for the reason that it is the day that the Manna began to fall in the desert. God provided the manna to sustain the Jewish people for the forty years that they were in the desert.[1] It is also the day on which Rabbi Shimon Bar Yochai received semicha from Rabbi Akiva.
[1] Chatam Sofer, YD 233.