From what I understand, you could never have 2 players using the same hero, even if you have multiple copies of the core set or an adventure pack. They are unique, and only one copy of a unique card can be in play at any given time.
Then I see this phrase in the UNofficial FAQ, under the entry for Dunhere...:
"With the core set, there can only be one DĂșnhere in play" (bottom of pg. 3)
That seems to imply to me that there are game mechanics available in adventure packs that allow more than one Dunhere in play. What gives? Just strange wording? Why use the phrase "one Dunhere?"
GS