All of the same benefits that a smaller baby enjoys!
There is no age that breastfeeding suddenly stops being beneficial. I have even found, as my daughter has moved into toddlerhood (she'll be two in a week!) that nursing seems to provide a grounding point she can come to when she's feeling out of control. It sort of smoothes the emotional roller-coaster that marks the age. And there are still all the health benefits.
As far as what makes an extended nurser. I suppose it is a matter of perspective. I don't really consider my 2year old to be an extended nurser (maybe at 3, but not yet, certainly
). But there are those that think nursing a 6 month old is extended nursing.
I don't know for certain, but I think formula fed babies are generally given formula for at least a year. I don't know if they get formula after that.