Both The Truman Show and 1984 are about an individual under constant surveillance. Truman Burbank and Winston Smith have their every move watched by an outside party, limiting what they can and cannot do. Truman does not immediately know he is being watched until he starts noticing odd events such as a spotlight falling from the sky, but Winston is well aware he lives in a surveillance state, even risking the writing of a journal in order to have some privacy.
Both protagonists are also influenced by propaganda designed by an outside party to influence their behavior. Truman is dissuaded from trying to leave his hometown (which is really just a massive TV set) through printed and audiovisual material that stresses the importance of staying home. Winston is bombarded with the infamous "Big Brother is watching you" slogan everywhere he goes. Once again, the big difference is that Winston is aware that he is seeing propaganda, while Truman is initially unaware of this fact.
Love grants both protagonists a small measure of inner freedom as well. Truman falls in love with an extra named Sylvia rather than the woman the producers of the show intended him to be with, while Winston's affair with Julia goes against the anti-sex and anti-romance ethos of their society.
The biggest differences between these two stories are their endings and the targets of their criticisms. Truman manages to escape the controlled world of the TV show which has been his life, giving The Truman Show a happy ending. Unfortunately for Winston, 1984 has no such happy ending and closes with Winston brainwashed by the Party. The focus of the two stories is also different: The Truman Show is a criticism of the entertainment industry and the media, while 1984 is a criticism of totalitarian regimes.