1) In the 1960 Stanley Kubrick film Spartacus, Spartacus (played by an icy and heroic Kirk Douglas) is an effective presentation of the character within the context of the film itself. Douglas' steely presence, indicated by his fierce eyes and imposing physicality, shows a character of immense strength and courage. He is a man of action, using few words, especially in the beginning, to convey his inner thoughts; like many slaves, his thoughts turn only to survival, lashing out with an economical sense of force in the many gladiatorial training and battle scenes he is to endure throughout the film. His aged, weathered face is a deep well of emotion, and he successfully conveys the sense of leadership that leads him to victory in the end against the Roman Empire and his nemesis, Crassus (Laurence Olivier). At the very least, the film is well-served by this portrayal of Spartacus, as a noble and sensitive leader whose command of love and loyalty from his troops is inspirational to him and to Crassus alike. His love story with Varinia (Jean Simmons) is also sensitively portrayed, with Douglas emitting a deep well of masculine energy.
In order to determine how well the character is adapted from its source material, it is necessary to understand that the film itself was based on Howard Fast's 1951 novel of the same name. The story itself loosely adapts Spartacus' real tale (which is still roughly shrouded in mystery) into the narrative required for the book and film - real details of Spartacus' life, such as his death (most likely in battle, not being crucified) are embellished and changed for dramatic effect. Looking at the film by itself, it is clear that the film's themes were updated for a contemporary setting - the film turns Spartacus into a literal Jesus figure, starting from nothing, struggling for an ideal and the freedom of others, leading his soldiers/disciples into a great victory, then being crucified for their sins.
The film's status as the film that broke the Hollywood Blacklist (screenwriter Dalton Trumbo actually uses his real name in the credits) suitably informs the film's themes; the "I'm Spartacus" scene, where everyone takes on a single name, is especially telling in a film whose screenwriter stops using a pseudonym. Douglas' single tear at the end of the scene, his tacit endorsement of the bold move that just happened, makes Spartacus an integral character who cares deeply about the freedom of others (which may not have been strictly true either). Furthermore, it shows a great deal of solidarity that was simply not present in Spartacus' real life - historical accounts note a significant amount of internal conflict between Spartacus and Crixus, his lieutenant, which is not present in the film.
However, in the end, the thematic messages that are infused in the film overshadow the need for historical accuracy in the film. Douglas is effective as a performer, and the idealized version of Spartacus provided in the film is suitable for the film's intended themes of oppression, poverty, freedom and enslavement - Spartacus needed to be a saint, in order to make his victory (and eventual sacrifice) all the more intriguing. The character needed to inspire universal love in order to explore the consequences of that kind of devotion (as well as Crassus' confusion and envy at that same adoration).
2) The characters of Crassus and Julius Caesar in both the 1960 Kubrick film Spartacus and the HBO series Rome (particularly its first episode) are quite different in many respects. For one thing, Crassus is completely absent from Rome; he never appears, and it is implied he is long gone by the time the series begins. In Ancient Roman biographies, Caesar died in 54 BCE, while Crassus died in 52 BCE; the fact that Caesar (Ciarian Hinds) is alive and Crassus is nowhere to be found indicates a desire by the showrunners to provide a unique focus on Caesar instead of Crassus, and so they needed him out of the way narratively in order to make that work.
As for Julius Caesar, the Kubrick film and the HBO series show some remarkable differences between the two characters. John Gavin, who plays Caesar in the film, is a young tactician at the top of his prime, learning from Gracchus (Charles Laughton) the ways of political machinations and dishonest maneuvering. He is directly contrasted with his friend Crassus, as he at first believes that Crassus is noble for having such a rigid outlook; it is only after joining Crassus that he starts to eclipse the man (something that Crassus is concerned about). Gavin plays him with a naive sort of strength, and a nobility that belies his later reputation as a master politician. However, historical accounts show that Crassus, Pompey and Caesar weren't allied until much later in history than the Third Servile Revolt; Caesar was never in command of the Roman garrison (in fact, it didn't even exist until Caesar himself created it). These changes serve to establish Caesar as a much stronger presence than he really was during this time; because of his fame in history, the filmmakers likely wanted to include him more prominently in the events of the film.
This portrayal is directly contrasted with that of Ciarian Hinds, who plays Caesar in the first episode of Rome. In Hinds' portrayal of Caesar, which happens near the end of his career (Hinds only lasts the first season before he is assassinated), he is a weary yet endlessly inventive manipulator. In one of his first scenes, the King of the Gauls is brought before him; Caesar forces the man to kiss the Aquila of the 13th Legion after stripping and kneeling, showing this Caesar to be a man of cool, collected malice. When Caesar learns that his daughter Julia has died in childbirth, he is somewhat pensive, as he merely considers what that does to the family line and the link that he has to Pompey. In fact, later in the episode Caesar is shown writing to Atia to find a replacement woman from within the family to replace that familial link.
Hinds plays up the villainous aspect of Caesar, who then becomes despondent when the symbol of the eagle is stolen from him; this demonstrates the purely symbolic nature of Caesar's power, which the filmmakers demonstrate is Caesar's only weapon. Of course, according to historical accounts, the stealing of the eagle is actually quite important; if the eagle was lost, Roman law dictated that the legion should be disbanded. Hinds' intense and dark portrayal of the character fits in with the creators' vision for a dark and gritty Rome for their show; playing the politics and drama naturalistically and gruesomely, Hinds' Caesar has a great deal of pathos and complexity, which suits a drama of that scale.
Apted, Michael (dir). "The Stolen Eagle." Rome, Season 1, Episode 1. HBO, 2005. Television.
Kubrick, Stanley (dir). Spartacus. Universal Pictures, 1960. Film.