The Plot Thickens basically adds more opportunities to link players together, thus creating longer and more complex chains of information.
What I mean by chain of information is something like this:
- Player A and Player B both were on a failed mission.
- Player B knows Player C's role card.
- Player C has declared players D and E to play success cards, but their mission with player A failed.
Chains make it easier to deduce information, thus making the Resistance players' role easier. But of course, experienced Spy players can learn to work with, or around, such cards, to confuse people even more.
Tl;dr: The Plot Thickens makes the game more balanced.