There are some big-picture similarities. For instance, both plays deal with regicide. But more than that, they deal with valiant warriors (Brutus and Macbeth) who are manipulated by power players (Cassius and Lady Macbeth) to strike down a king that they actually liked or respected. In both cases another valiant warrior (Antony and Macduff) arrive to avenge the death of the true king.
In both cases, the death of the antihero (Brutus and Macbeth) is a foregone conclusion. Both men see it coming (Brutus for longer than Macbeth, who doesn't realize he's doomed until we find out that Macduff was born by C-section) and want to die nobly in battle. Macbeth succeeds in that he falls in combat to Macduff; Brutus succeeds in committing the Roman equivalent of seppuku.
Another similarity involves the deaths of the spouses of the antiheroes. Where Lady Macbeth is one of the most active forces of malice in the play, she gets a bit hinky (sleepwalking scene anyone?), then dies off stage, evidently by suicide (Malcolm later states that word is that Lady Macbeth killed herself - violently). Portia, the faithful spouse of Brutus, is obviously a more feeble sort of woman from the start, as references are made to her questionable state of health and she's all swoony. She also kills herself off-stage, reportedly by eating fire. Jenn Hubbard (
Yet another similarity involves the presence of independent practitioners of supernatural arts. The Scottish play opens with three witches, who foretell what is to be. That they purposefully withhold at least some of the information from Macbeth is part of their charm, and a large cause of mischief in the play. Julius Caesar involves a soothsayer, who hollers "BEWARE THE IDES OF MARCH!" at Caesar, along with supernatural portents (a severe, massive storm; lions whelping in the streets; cats & dogs, living together; etc.) and word from augurers (who have done some sort of divination involving ritual sacrifice). Where the plays diverge is that Macbeth listens to his portents when he ought not, and Caesar doesn't listen when he should. As pointed out before, Caesar, like Hamlet, "defies augury." (In an aside, where Macbeth and Hamlet intersect involves one of the superstitions about the play. One of the "cures" for having said the name of the Scottish play inside (or near) a playhouse when not in performance or rehearsal is to say "Angels and ministers of grace defend us." (Hamlet, Act I, sc. iv.) But I digress.)
Also in common? Sleeplessness. In Julius Caesar, you have Brutus talking about how he hasn't slept since Cassius first wound him up about Caesar; in Macbeth, you learn that Macbeth "hath murdered sleep". Sleeplessness is closely aligned with a guilty conscience in both cases. Lady Macbeth doesn't sleep well, either, but walks and talks in her sleep, obsessing over the bloodstains she imagines on her hands.
If the play had only one or two of these similarities, it would seem more accidental to me, but I think these are themes Shakespeare enjoyed exploring (for whatever reason - some say it's a subtle swipe at a repressive society), and that he enjoyed weaving these particular story fronds together in his work. Tomorrow: On to another play!