One of the best hospital chaplains I know was also a hospice chaplain. She has such a wonderful, comforting touch with people. I think doing hospital chaplaincy has to be a little easier, because not everyone you serve is going to die fairly soon. There are happy times.
A hospice chaplain also has to be prepared to serve those who do not profess a particular faith or belief in any deity. They still are compassionate, kind and comforting, regardless. Anyone who is a chaplain has to be sensitive to the idea that not everyone will believe as they believe, and some may even be hostile to those beliefs. But they still serve, anyway.