We do it in my OPA chapter. The bigs shower the littles with gifts, the families (each as a whole) shower the littles with gifts, and the littles are expected to get one gift for their bigs. Compared to the armload of stuff they get to take home after initiation, well, it's the least they can do, right?
I've had four littles. From the two at my local chapter, one got me a little charm with our family mascot, and the other got me a towel with the family mascot (a frog). My other two were at colonies, so because it's a local thing, bigs weren't given gifts.
At big sis revealing in Coyote, bigs didn't receive gifts. As far as initiation, I don't quite know yet...