George Orwell over time became fond of pointing out how polar-opposite ideologues are more similar than they realize. His essay Notes On Nationalism is devoted to it.
"The Catholic and the Communist are alike in assuming that an opponent cannot be both honest and intelligent."
Sometimes remarked upon as France and England. Both have Barbarian/Germanic origins for their cultures, with massive amounts of immigration. Both have had periods of complete military dominance. Both at one point had Normans in its landmass. Both have seen their countries invaded and desolated, be it the Romans or the Nazis, and their languages have evolved so closely that words such as 'regard' and 'W.C' mean exactly the same thing. It's almost as if the two countries are so similar as to be defensive of each other to outsiders...
France doesn't have "Barbarian/Germanic origins for [its] culture", since it's Romance. The first historian who actually emitted the hypothesis that the first Franks might have been Germanic instead of Trojan got thrown into the Bastille for insult to the Crown. The invasions by Franks (mostly under Clovis around 500) and that of William (1066) are comparable in certain respects, but they wildly differ regarding the cultural impact of the invaders (on one side romanized Germans invading Romans, that is invaders being aware of their alleged cultural inferiority and integrating virtually immediately; on the other Gallicized Vikings herding French troops invading Germans, you know how it went). It should be noted that France actually never underwent a massive amount of immigration between the Neolithic and the 20th century. Nor did Britain, even though the Angles drove out something like 100-200,000 Britons.
As has been pointed out in histories of the Wars of the Roses Richard III was demonized by the Tudors as a usurper who illegally took the throne and killed of rivals with a better claim to the throne then him. Henry VII had an even worse claim to the throne, usurped Richard, then proceeded to eliminate others with better claims then him, which continued even in the time of his son Henry VIII.
Joseph Stalin and Adolf Hitler were Arch Enemies and at opposite ends of the political spectrum, but they were also similar in a lot of ways, beyond the obvious of both being brutal dictators. They both had artistic ambitions (poetry and painting), both had criminal pasts and did time in prison (for bank robbery and treason), both were born on the fringes of their future empires (Georgia and Austria), and both were vastly underestimated by the establishment until they suddenly broke through and revealed themselves to be much more dangerous than everyone believed (Stalin was a minor Bolshevik party functionary who managed to systematically take over, and Hitler was the leader of a tiny nationalist political party who the leaders of the Weimar Republic saw as a handful of disaffected nobodies).
During the Greek Debt Crisis, Germany refused to give any consideration to Greece and its economy regarding its debts to the European Union, refusing to back away from austerity citing principles and probity. The French economist Thomas Piketty called them out by reminding them that Germany has never repaid its debts to other countries and indeed repeatedly recieved debt-relief measures from Allied nations to help them rebuild their economy, and furthermore has a history of extorting debt without ever honoring their committments.
This article on Cracked points out the surprising similarities between Gangstas and Rednecks.
The Blue Code of Silence, in which police officers resist testifying against each other, is sometimes compared to the Mafia's Omerta code of silence.
A turning point in the Civil Rights movement happened when a breaking news bulletin about a racial march interrupted a documentary, showing police attacking the marchers. The problem was that the interrupted documentary had just shown Hitler's goons doing the same thing to the German Jews. Viewers found the similarities very disturbing.