Where the tzadik meets the wider comparative subject is at the grave. Visiting the tombs of the righteous is an old Jewish practice, attested long before Hasidism, and Josef Meri's work on medieval Syria shows Jewish and Muslim visitation running side by side at overlapping sites. Hasidism intensified it. The anniversary of a tzadik's death, the hillula, is kept as a gathering at his tomb rather than as a day of mourning, and the largest of these are very large indeed.
Two are worth naming because the atlas already holds the figures. The tomb attributed to Shimon bar Yochai at Meron in the Galilee draws a mass gathering on Lag BaOmer, with bonfires, music and the first haircutting of small boys; the attribution of the site is traditional and the association of Shimon bar Yochai with the Zohar is itself a scholarly dispute of long standing. The grave of Nachman of Breslov at Uman in Ukraine draws tens of thousands of men at Rosh Hashanah, on the strength of a promise his followers record him making about those who come to him there, and the pilgrimage continued through Soviet prohibition and has continued through war.
The comparison with Muslim ziyara and with Christian pilgrimage to relics is close enough to be useful and different enough to be worth stating carefully. In none of the three does the tradition's own theology describe the dead person as an object of worship, and in all three that has been the accusation made from outside and, more sharply, from inside.