We do both in our house. My kids get one present for each night of Hanukkah. Usually one night they will open gifts from my parents, and another night gifts from my sister. If any other relatives of mine send a gift (sometimes they do, sometimes they don't), that will count as another night. My husband and I give them the gifts for the remaining nights. Usually, I give them one bigger gift and the rest are small. A small gift would be one book, or piece of clothing, art supplies, etc.
For Christmas, they get a big gift from Santa, a couple of small/medium gifts from me and my husband (board game, books, clothes, DVD, video game... not necessarily all of those, but that type of item), and a stocking filled with small stuff. They also get gifts from my husband's parents and brother for Christmas.
It is a lot of gifts, but I try to not make it a million toys. This year, lots of their gifts are clothes and books, because our house is overrun with toys! I want them to grow up with 8 nights of Hanukkah like I did, and my husband wants them to have Christmas, even though it wasn't that big of a thing in his house growing up.
My son is 5 and my daughter is 2, and this has always worked well for us.