All three have fantastic biographies/military histories by Theodore Ayrault Dodge, and it was reading these that I first came across the almost eerie parallels between Alexander and Caesar.
Both men were born into good families (in Macedon the kingdom was theoretically hereditary but it was pretty common for an uncle of a king to take over, as Alexander’s own father did). Alexander played an instrumental role in the Battle of Chaeronea at 17, slaughtering the elite Theban Sacred Band, and became king at 19 until his death just over a decade later. Caesar was a slower starter (it is scarcely possible to be faster) but he too rose to become the undoubted leader of his armies and effectively became a king.
The two generals led elite military forces that grew accustomed to unprecedented success under their leaders. Alexander clearly had the greater achievement, in my view. After centuries of fearing the overwhelming power of Persia he led the Hellenistic armies to total victory, scoring staggering victories and reducing every city that dared defy him by expert siegecraft (Tyre being particularly impressive). However, Caesar also had a great military record, finally exorcising the ghost of the Gauls who had ravaged Rome centuries earlier.
Neither man truly knew defeat on the battlefield. Caesar did not enjoy unmitigated success, but his record is nevertheless excellent. Alexander’s feats almost defy belief and he was a legend even in his own lifetime.
However, both men died premature deaths. Alexander probably died of a fever, although there is a suggestion that Antipater (who ran Macedon in Alexander’s absence) had Iollas, his son and the king’s wine-pourer, poison him. Caesar, rather famously, got stabbed to death by a large number of people.
Sadly, there’s a rather more gruesome coincidence between the two. Caesar’s son was called Ptolemy Caesarion, and was executed by Octavian (who became Augustus) before his 18th birthday. Alexander’s son was officially king, but regents ruled in his stead. He was killed by Cassander, ruler of Macedon, when some claimed a 13 year old could rule on his own.
Ironically, both men, who barely knew defeat in their military careers, died younger than Hannibal (who lost the Second Punic War). Neither of their sons succeeded them and both defeated a great foe (admittedly, Caesar did slaughter his own side).
Both chaps also had epilepsy, which is a rather strange coincidence. [Hannibal was also disabled, but he had one eye, having lost one to exposure during the perilous march through the Arnus Marshes].
There were some rumours that Caesar was also friendly with fellows, as Alexander famously was, but there’s some doubt about that.
So, unusually, both chaps had epilepsy, both died prematurely, and neither were succeeded by their sons (both of whom were murdered). It is possible both were murdered and partial to man-on-man action, but the former is uncertain regarding Alexander and the latter regarding Caesar.