Darth Bane is the Anti-Luke

In an interview about season six of the clone wars, Filoni says this about Bane:
"I wanted it to be special, and to have him come in and be Darth Bane — the anti-Luke in so many ways "

In this thread, I will ponder the examples and implications of this statement.

It was said the same about Ulic-Qel Droma.

"There's somewhat of a connection to Luke. As a matter of fact, Ulic is sort of an anagram of Luke. This guy ends up going totally over to the dark side. So the idea is, we take the young, idealistic hero, don't make him look like Skywalker, make him a different person, but the definite type—the impulsive, young warrior who's very sure of himself."
-Tom Veitch

Power
Darth Bane and Luke are both the most powerful people to exist in their respective eras, barring the Ones.

An implication of this being that as Luke's Sith counterpart, Bane is very powerful.

Both Rebuilt Their Respective Orders
After their respective order's destruction (Sith for Bane, Jedi for Luke), both rebuilt their orders, essentially reshaping them and getting rid of the dogmatic views of their predecessors.

After the Old Jedi Order's destruction by the Great Jedi Purge, Luke began the new Jedi Order, and essentially reformed it. Luke did away with much of the ritual and formality that ran rampant within the Old Jedi Order, placing more emphasis on individual experience, allowing the New Jedi Order to be less centrally controlled, and getting rid of mandatory superfluous details such as the mandatory wearing of Jedi robes. In my opinion the best change brought on by Luke in his New Jedi Order was the embracement of emotion. The Old Jedi Order taught that emotions were a thing to be suppressed, while Luke understands the value of positive emotions, and thus implemented them into his order.

After the Brotherhood of Darkness's destruction by the thought bomb that Bane so "generously" provided them with the ritual for, Bane reformed the very flawed Sith into an order of cunning, secrecy, ambition, and power. The Brotherhood of Darkness preached equality (despite Kaan secretly controlling and mindfucking everybody), which Bane knew to be contradicted by the nature of the Dark Side itself. Not only did Bane correct upon the Brotherhood's mistakes, but he also corrected upon the mistakes of all of the previous Sith Orders. The mistake that the Brotherhood attempted to correct but ended up replacing it with a whole new problem, was infighting. For examples of this, look no further than the scheming and betrayal between the original Sith Lords, or the rivalry between Kressh and Sadow when the two were supposed to be leading an army to victory, or Malak's betrayal of Revan, or the petty squabbling and Sith politics of the Dark Council when they were supposed to be destroying the republic, or the civil war that tore apart Ruin's empire, or the fighting between the factions that splintered off of Ruin's now destroyed empire. Each and every time, infighting would weaken and bring down the order, however to remove infighting removed the right to rule from the strongest individual and instead reduced them to being equal with their contemporaries. Bane instead implemented Sith fighting and ambition into a system that strengthened and preserved the order rather than weakening it. Through the Rule of Two, the master and apprentice would operate in secrecy, building up a base of knowledge, wealth, and political control, while the apprentice ambitiously trained to one day take down their master. The apprentice would one day challenge the master, and the winner would train a new apprentice. Of course this system could be cheated and was cheated many times, however the ambition and training to overthrow one's master kept the order strong, even if a successive master wasn't necessarily more powerful than their predecessor. All the meanwhile the Sith powerbase grows in secrecy until two of these very powerful sith are ready to exploit it and destroy the Jedi.

Both rebuilt their respective Orders, and corrected the inherent flaws of each of their predecessors relative to their specific sides of the force. Luke reintroduced the value of positive emotions to the Jedi and granted them a measure of equality and freedom more representative of the light side of the force, while Bane, instead of contradicting the dark side to correct it's inherent flaws, implemented those supposed flaws into a system that reaped their benefits while placing a check on their internal damage.

Fighting Styles
Luke and Bane's fighting styles both contain largely the same roots: Djem So as their primary form, Soresu as their defensive form, and a third all offensive form (Ataru for Luke and Juyo for Bane). Despite the similar roots of their styles and the fact that both are highly effective in combat, they both utilize those roots and techniques in very different ways. Despite how much Bane's offense and defense compliment eachother, the two are two very different and distinct things. Luke on the other hand combines his offensive and defensive forms together in something of an amalgamation of all of his techniques. Neither of these is inherently superior to the other, however they are distinctly different and are very reflective on the philosophies of each and their respective sides of the Force. Bane's fighting style contains a lot of extremes, reflecting the intense and extreme nature of the dark side and the Sith, while Luke's fighting style does not contain these extremes, but rather works his forms together into one, reflecting the harmonious nature of the light side and the Jedi.

Disgust For Eachother's Force Alignment
Luke views the light side of the force as a means to help others, and as a way for people to persevere together, and believes that the dark side corrupts everything it touches not understanding why people who know this would choose the dark side.

Bane on the other hand views the dark side as a means for individual power, and breaking free from restrictions, while he views the light side to be corrupting through its lie of equality and emphasis on restriction, both of which he considers to be chains holding back those who are truly powerful.

A lot of this diametric opposition between Luke and Bane is demonstrated in Bane's section of the Book of the Sith where Bane mentions the power of the dark side, and Luke leaves quite snarky side notes next to Bane's writings. Bane extolls the glory and power of the Darth title, and what it means to his order, and Luke expresses happiness that his family ended it. Bane claims it is better to find apprentices young so they won't be corrupted by the Jedi, and Luke says it's important for the Jedi to find them first so they can learn to help others. Bane describes practical use of the force for combat, Luke smugly states that even the aggressive forms of the Jedi emphasize defense while the Sith only care for attack. Bane emphasizes emotion over peace in a fight, Luke claims most Sith lose because they lack peace. Bane brings up the practicality of mental attacks, Luke implies the Sith as being inferior for only see the negative. I think you get the idea here.

Immortality
Both Luke and Bane agree that living forever is the desire of selfish assholes, however their reasons for this are quite different. Bane believed that when one's apprentice surpassed them, they became expendable and deserved to die. Luke on the other hand believed that everybody had their time and that nothing good came from trying to cheat it. Bane's reasons for condemning those who seek immortality were based on the principle of power, survival of the fittest so to speak, while Luke's reasons were based on equality, the belief that everybody has their allotted time in life regardless of their power.

Sharing Power
Luke believes that it is the responsibility of himself and his order to share power and help others. Bane on the other hand, believes that sharing power is an act of weakness and a violation of the Sith Code.

Descendents
Both Luke and Bane left behind descendents after their death in a way. Bane left behind his Sith order, and the rest of the Banite Sith from Zannah to Sidious in a rich chain of teaching and knowledge. A dynasty of evil, so to speak. Luke left behind his own literal descendents from Ben to Cade, in a lineage of powerful Jedi who have saved the Galaxy on numerous occasions. Both of their legacies and descendents have continued to shape the events of the Galaxy long after their deaths and will for the foreseeable future...