I've heard the sympathiser in Pegasus Expansion is far more interesting to play than the one in the basic game. What makes it so different?
For context: In basic BSG, as you know, in 5-player, the ratio between humans to Cylons is 3-2. This usually results in interesting, difficult-but-not-impossible skill challenges and a tense game.
By contrast, in 4- or 6-player, the sympathizer can be on either the human or Cylon team, depending on whether or not the humans have any resource in the "red zone." during the Sleeper phase. While being low on a resource might seem bad, it's not as bad for the humans as being in a 2-2 or 3-3 situation. After the Sleeper phase, the game tends to be a blowout--especially if the Cylons get the sympathizer, where the humans will have enormous difficulty making enough skill challenges. The faction of the sympathizer becomes so important that savvy players will engage in a weird metagame where Galactica's resources must deliberately be sabotaged for the good of the humans!
Some people also feel that having a known player whose loyalty is unquestioned takes away from the drama of the game.
By contrast, the Pegasus rules: The sympathizer is definitely a Cylon, but receives a card from the Sympathetic Agenda deck. This card determines which side the sympathizer is actually on, and furthermore gives the sympathizer a secret agenda that must be achieved for the sympathizer to win. These agendas are (mostly) tuned to create a close game where both the humans and Cylons will distrust the Sympathizer. For instance, the Grant Mercy agenda requires the Humans to win, but requires Food, Population, or Morale to be at 2 or lower--if the "friendly" Cylon tries to advance this agenda, the humans may treat him as an enemy!
Not only does this create closer games, but instead of the sympathizer's loyalty being unquestioned, it is instead a complete mystery up until the very end (or unless a set of very experienced players who are familiar with all the agendas suss which one the sympathizer has, I suppose.)
If you're not familiar with Pegasus, it's important to mention that the expansion also contains rules for a Cylon character infiltrating Galactica and playing more as a normal human character than a base-game Cylon just wandering around the Cylon fleet, so the question of the characters' trust or mistrust towards the Cylon becomes important. If you are interested in the details, the rulebook is here. (Sympathetic Cylon rules on p. 18, rules for infiltrating on p. 11)