This is Vic Wertz's reply to a similar question at the Paizo site at:
Vic Wertz at Paizo wrote:
Characters are intended to be compatible with any set. That said, some characters may have advantages in one set that they lack in another. For example, the gunslinger Lirianne from Skull & Shackles would not be as useful in Rise of the Runelords unless you *also* add in some firearms for her to use. And many Skull & Shackles characters have ship-themed powers that would not be useful in an Adventure Path that lacks ships, though most of their powers will be useful. On the other hand, we have laid some groundwork for the future—you might have noticed that some cards in Rise of the Runelords refer to the Craft skill, which no RotR characters actually have—but some S&S characters do!
On that same page, he also says:
For returning characters, the base cards have small differences, and the role cards are very different.
You should use the role card that comes from the same set as your character card. Remember that role cards are placed over character cards, and they include the powers from those character cards, so if you were to mix-and-match, you would have issues with those powers not matching. Which is to say the S&S role cards are designed to advance S&S characters, and the RotR role cards are designed to advance RotR characters.