Based upon my preliminary research we have three cases that manifest Pirsumei Nissa in Halachah - [perhaps there are more?]
A. Ner Hanukkah
B. Megillat Purim
C. Arba Kossot
We have several Halachot flowing from this designation
1. "Af hein hayu b'oto hanneis" implies gender equality in the performance of all of the above Mitzvot
2. We are also enjoined to "sell the shirts off our backs" to fulfill these Mitzvot
• Women are usually enjoined from drinking too much wine. Obviously this is suspended during arba kossot
• However, re: Megillah, it seems that many Posqim refuse to waive issues of "kol ishah" to permit women to read the Megillah in Public.
Perhaps the Hilluq is the private nature of the Seder vs. the public nature of Megillah
• Another anomaly is that re: Ner Hanukkah, husbands and wives usually fulfill this jointly. This may be driven by the "uveito" nature of the Mitzvah which pertains to the household [heftza] as opposed to the individuals [gavra].