There are no significant differences between the tradition of Sephardic and Ashkenazi Jews regarding Hanukkah. There are only some minor variations.
Some illustrations:
THE FUNCTION OF THE SHAMASH
According to the Ashkenazi custom, the auxiliary candle or shamash is lit first. Thus, after saying the berakha one lights the rest of the candles with the Shamash, and after lightening all candles, one deposits the shamash in its place. The Sephardic tradition, however, is to light all the candles with a match or a separate candle, and only at the end is the shamash lit. Whereas for the Ashkenazi tradition, the shamash is also used to light the candles, in the Sephardic tradition, it is not; since the main reason the shamash is lit is to avoid a benefit from the light of the Hanukka candles, in case we involuntarily use the lights of those candles. In other words, whereas for the Ashkenazi tradition, you use the “flame” of the Shamash -to light other candles- for the Sephardic tradition, the Shamash is used just for its “light”.
WHERE SHOULD YOU PLACE YOUR HANUKIA?
Many Sephardic families, especially in Israel, keep the original custom of lighting the candles outside the house, on the opposite side of the Mezuza (as seen in the picture above). The Ashkenazi tradition, however, is to light the Hanukiah (aka “menora”) inside the house, near a window, so that it can be seen from the outside.
HOW MANY HANUKIOT WE LIGHT?
In many Ashkenazi communities, the custom is that each family-member lights their own Hanukiah, even young children, once they are older than six years. In Sephardic families, however, it is customary to light only one Hanukia per family (מצוות איש וביתו). This is similar to the case of Shabbat candles: whereas according to the Sephardic tradition, only the mother lights the Shabbat candles; according to the Ashkenazi tradition, each of the daughters in the family lights their own Shabbat candles.
LEHADLIQ NER HANUKKA or NER SHEL HANUKKA?
According to the Ashkenazi tradition in the Berakha, one says: “lehadliq ner SHEL Hanukka”, (… to light the Hanukka candle). While Sefaradim says, following the words of the Shulhan ‘arukh: “lehadliq ner Hanukka”, omitting the word “SHEL”. There is no grammatical or semantic difference between these two versions. And one can not say that one version is correct and the other is not. Actually, the original version of this berakha (Maimonides, MT Hanukkah 3: 4) is “lehadliq ner SHEL Hanukka”, similar to “lehadliq ner SHEL Shabbat”. The Sephardic tradition, which generally follows Maimonides, is based, in this case, on the opinion of the Mequbalim. Some Sefaradim, however, for example, those of the Hispanic-Portuguese community of England (which interrupted the practice of mystical-based traditions the events Shabbetai Zevi) and some old Sephardic Siddurim such as Tefilat haHodesh or Bene Tsion, have retained the original version of Maimonides which includes the word “shell”, and so was the tradition in Iran (Mr. Nassim Bassalian).
TRADITIONS
Playing the sebibon (dreidel) is an Ashkenazi custom that Sephardim never practiced. Same as Hanukka Gelt (coins or gifts for children).
