Reb Nachman of Breslov revealed a wondrous secret of the greatness of Rabbi Shimon bar Yochai at the very beginning of Likutei Mohoran:
Rabbi Shimon bar Yochai (Rashbi) assured us that Torah would never be forgotten from Klal Yisroel. The Gemara (Shabbos 138b) relates that when the Rabbonim came to Kerem Beyavneh, they said that in the future Torah will be forgotten from Yisroel. Rashbi, however, said that the Torah will not be forgotten, as it says (Devarim 31, 21): כִּי לֹא תִשָּׁכַח מִפִּי זַרְעוֹ – "for it will not be forgotten from the mouth of your children". And, like it says in the Zohar (Naso 124b) that with this very work, the Sefer HaZohar, we will go out from exile.
And now come, see and understand the wondrous secrets of our holy Torah! The reason why Rashbi's assurance that the Torah will not be forgotten is based on the posuk כִּי לֹא תִשָּׁכַח מִפִּי זַרְעוֹ is because the secret to the assurance is hidden in this very posuk. The last letters of these words: כִּ׳י לֹ׳א תִשָּׁכַ׳ח מִפִּ׳י זַרְע׳וֹ – "for it will not be forgotten from the mouth of YOUR children", spell יוחאי, as if to say that the child of the one referred to in the verse will guarantee that the Torah will never forgotten. Rashbi hinted that through the children of Yochai, meaning himself, Torah will not be forgotten. He authored the Zohar and it is precisely through the Sefer Zohar Hakadosh that we will return from exile.
And know that the secret of Rabbi Shimon himself is alluded to in another posuk (Daniel 4, 10), because know that the Tanna Hakadosh Rabbi Shimon is the aspect of : ע׳ִיר וְ׳קַדִּישׁ מִ׳ן שׁ׳ְמַיָּא נָ׳חִת, a holy angel came down from Heaven - the first letters spell שמעון.
This alone could explain why specifically the Yom Hillula of Rabbi Shimon bar Yochai is celebrated with such pomp and festivities.
There are many connections between Reb Nachman of Breslov and Rabbi Shimon bar Yochai. Interestingly, the numerical equivalent of רבי שמעון בן יוחאי is exactly equal to that of רבי נחמן בן שמחה. The yartzeit of Reb Nachman of Breslov always falls out on the same day as the previous Lag BaOmer and Zayin Adar, the yartzeit of Moshe Rabbeinu (Kochvei Ohr)
See also: Lag BaOmer - Segulas & Minhagim
תורתו מגן לנו היא מאירת עינינו הוא ימליץ טוב בעדנו אדוננו בר יוחאי
Your Torah shields us, it lights up our eyes!
He will advocate good for us, Our master - Bar Yochai!