How prominent are Sephardic Haredim in the Jewish world? What are their differences (beside origin) from Ashkenazi Haredim?

It seems in popular perception, Ashkenazi Haredim are represented the most among the Haredim, but how prominent are their Sephardic/Mizrahi counterparts in the Jewish world? How do they differ in tradition, and do they comprise a significant portion of Haredim?