A chant or praise used at Passover or Hanukkah?

The blessings recited on Hanukkah are completely different from the blessings recited on Passover.

The 3 Hanukkah blessings are only for candle lighting, there are no others.

When you light the candles you say:

"Ba-ruch A-tah Ado-nai E-lo-he-nu Me-lech ha-olam a-sher ki-de-sha-nu be-mitz-vo-tav ve-tzi-va-nu le-had-lik ner Shel Cha-nu-kah." (Blessed are You, Eternal our God, Ruler of the universe, who has sanctified us with Your commandments, and commanded us to kindle the Chanukah light.)

You also recite:

"Ba-ruch A-tah Ado-nai E-lo-he-nu Me-lech Ha-olam she-a-sa ni-sim la-avo-te-nu ba-ya-mim ha-hem bi-zman ha-zeh." (Blessed are You, Eternal our God, Ruler of the universe, who performed miracles for our forefathers in those days, at this time.)

And on the first night only, you recite the prayer for a special occasion:

"Ba-ruch A-tah Ado-nai E-lo-he-nu Me-lech Ha-olam she-heche-ya-nu ve-ki-yi-ma-nu ve-higi-a-nu Liz-man ha-zeh." (Blessed are You, Eternal our God, Ruler of the universe, who has granted us life, sustained us, and enabled us to reach this occasion.)