It is often remarked that Sasuke is the "Kakashi" of Team 7. But aside from both being introverts, these two really couldn't be more different and they have very little in common.

Sasuke's story is about someone allowing their pain to lead them to hurting others, whereas Kakashi's story is about someone allowing their pain to stop them from helping others. There are many moments where Kakashi could have taken action with compassion, goodness, and sensitivity. Instead, Kakashi let his futility complex and apathy weigh him down and stop him from helping others, even while having three kids desperately depending on him. Kakashi didn't help his students when they needed it most.

There are some parallels between Kakashi's and Sasuke's stories if you care to look for them, but a few congruencies in their background stories doesn't equate to being alike. Otherwise, you might as well say that Kakashi and Sasuke are just like every character in the series because I could find traits they have in common with just about every character in Naruto's cast if tasked with doing so.

Fans often say that "Kakashi = Sasuke" and enjoy comparing Team Minato and Team 7, but generally speaking, all of the teams in Naruto have the same team structure that follows this basic formula: there's the lively, brash, talkative, nice, upstanding guy who is usually an underdog; there's the cooler, quiet, serious guy who is exceptionally skilled/talented and smart, prodigious, practical-minded, and commonly a bit rude or strict; and there's the (generally exuberant and outgoing) girl who can be fiery but also caring and she usually has a crush on a guy. Virtually all of the Naruto squads can be categorized into this basic pattern, more or less:

Naruto – Sasuke - Sakura

Kiba – Shino - Hinata

Choji – Shikamaru - Ino

Lee - Neji - Tenten

Obito – Kakashi - Rin

Kankuro – Gaara - Temari

Jiraiya – Orochimaru – Tsunade

Suigetsu – Jugo – Karin

Tenma – Itachi – Shinko

Hiruzen – Homura – Koharu

Yahiko – Nagato - Konan

Team 7 has no more in common with Team Minato than it does with any other team in the series. Nearly every team has a similar basic structure in regards to personality types. Fans act like it's special that Team 7 is reminiscent of Team Minato, but Team 7 is about as similar to Team Minato as they are to every other team. There are a few vague and loose similarities if you purposefully look for them, but I don't see much of a point in comparing Team 7 to Team Minato unless you are specifically discussing parallelism.

The love triangle is also drastically different from Team 7's dynamics, and not congruent at all. Team 7 is a case of two boys being in love with the same girl, and Team Minato is a case of the same girl being in love with two boys. Both Naruto and Sasuke loved Sakura, but Sakura didn't romantically love Naruto, so she ended up with the guy she was in love with, Sasuke. On the other hand, Rin loved both Kakashi and Obito, but could only choose one (and I think it's clear she would have ended up with Obito, had not tragedy struck the team). ObiRin is more reminiscent of NaruSaku, which wasn't canon, than SasuSaku.

The only real similarity is Obito, as Naruto and Obito do have a surprisingly high amount in common in regards to their personalities, more so than typical. But Rin and Sakura couldn't be more different, just as Kakashi and Sasuke couldn't be more different.

Sasuke and Kakashi have quieter, cooler, calmer temperaments, but so do like half of the Naruto cast, so I don't see how this makes Kakashi and Sasuke alike. They are both introverts, but even the way they are introverts is vastly different. Introverts have a lot of variance between them. Some introverts are more introverted than others, and there are many different categories of introverted personalities. We might as well call Orochimaru and Sasuke and Neji as all being "similar" if we're looking for "similarities" between characters.

Nothing between the teams is the same, except for Naruto and Obito shared a few congruencies, but even they are quite different people when you really get down to it.

And Kakashi's and Sasuke's personalities aren't even alike.

Sasuke is daring, imaginative, rebellious, passionate, emotional, reckless, ambitious, introspective, thoughtful, perceptive, determined, persistent, focused, aggressive, and he questions things.

Kakashi is calm, placid, easy-going, low-energy, contemplative, perceptive, dispassionate, passive, apathetic, irresponsible, directionless, brave, and he accepts the status quo.

As a kid, Kakashi was a by-the-book guy obsessed with rule-following. Sasuke is introduced as the complete opposite: Sasuke's first main action in the series was to disregard the rules as he famously did during the bell test, showing right away that Sasuke has little interest in following rules. On the other hand, kid Kakashi was obsessed with staying inside the frame of rules that someone else had built for him to follow. They were complete opposites in methodologies from a very early age.

Kakashi was a stickler for the rules who let his actions be ruled by hard, unfeeling logic. On the other hand, Sasuke never cared about following rules and is ruled by his emotions. He has lofty goals and vision, whereas Kakashi is unambitious and does not have any plans for the future.

Kakashi has a tendency to feel guilty and hold himself responsible for the misfortunes that befall others around him, but the way he responds to and processes his guilt is drastically different from the way that Sasuke deals with his own survivor's guilt. Sasuke turns his guilt into action, channeling those negative emotions into a purpose and objective, essentially weaponizing his strong negative emotions.

Kakashi doesn't channel or process through his emotions, but lets them stick inside and not go anywhere, nor do they take him anywhere. He doesn't try to change the world nor himself; he apathetically stagnates.

Sasuke is a raging inferno of fiery passion, and Kakashi is a placid pond, serene and unnaturally still. If Kakashi is stuck in a rut but unable to muster the energy to move forward, then Sasuke is stuck in a pit desperately trying to claw himself out or otherwise digging himself an even deeper ditch. Sasuke is constant motion and Kakashi is passive stillness. Whatever his situation, Sasuke will always take action for better or for worse, and whatever the situation, Kakashi will be lethargic and reluctant to take action.

Kakashi struggles with being locked in a feeling of futility and fated helplessness, whereas Sasuke believes in one's purpose and taking matters into one's own hands. Sasuke is a force of change and Kakashi is perpetually stagnant. This is true both in their external actions and internal psychology. Sasuke is a very dynamic character, constantly changing as he reacts to stimuli in the world around him and emotionally responds to it. Kakashi is a stagnant character, not reactionary to the world or the people around him.

Kakashi has a low internal locus of control and a fatalistic outlook. He believes everyone is just another cog in the machine, being turned in specific predetermined directions, helpless to fight against their fate. As a result, Kakashi lacks the spirit or willpower to take his life into his own hands and do something with it. He doesn't have a sense of agency strong enough for him to believe he can make a difference or change things for the better. When things go wrong for Kakashi, Kakashi may blame himself, but he also tends to blame others and external circumstances. He can't change himself nor can he change others or the cruel shinobi world, so he doesn't even try.

Kakashi responds to his grief and loss by shutting down and suppressing his emotions, cutting himself off from any strong feelings. Kakashi does his job because it's what he's supposed to do, but he takes almost no pleasure from life. He's a cog in the system, going through the motions without any real direction or desire to move forward. He's stuck in a rut and has no motivation nor ambition to get out.

Sasuke has a high internal locus of control and a strong sense of agency. He strongly believes in taking one's own destiny and purpose into one's own hands. If Sasuke fails in his goals, Sasuke doesn't blame others so much as he blames himself. Whenever he fails, he gets upset that he's too weak, and Sasuke treats his own weaknesses as unacceptable and unforgivable, which is why instead of doing nothing, Sasuke's throws himself into getting stronger as quickly as possible. Sasuke isn't fatalistic, nor does he see his efforts as futile or pointless. He's disappointed by his weaknesses and learns from them by realizing he needs to get stronger, but that doesn't leave him feeling like his efforts were pointless or meaningless – just that they weren't good enough and need improvement.

Sasuke is not a cog in a machine, he's the force propelling the machine. Unlike Kakashi, Sasuke doesn't shelf his grief along with the rest of his emotions and helplessly soak in the futility and helplessness of his own limitations. Sasuke is everything Kakashi isn't: ambitious, driven, passionate, and motivated. Kakashi is aimlessly wandering through life without direction and no chosen goal; Sasuke always has a plan and an objective. And if he doesn't have one, then he comes up with one on the spot. As soon as Sasuke completes one objective, he doesn't waste a second before moving on to the next. Sasuke is about as driven, motivated, and focused as a person can possibly be, and Kakashi is the complete antithesis of that. Kakashi could strive for more, could be more, could aim for more, but he isn't, because he doesn't try.

Sasuke views the world as full of meaning and purpose, that everyone has a role they are meant to fulfill and a purpose they are meant to pursue. Sasuke's struggle merely centers around the question of figuring out what his purpose is: Is it avenging his clan? Is it protecting Team 7? Is it destroying Konoha? Is it protecting Konoha? Is it saving the world? Is it killing Naruto? Is it allying with Naruto?

Sasuke sees the world as full of purpose and duties that one must fulfill, making his world full of meaning and purpose.

For Kakashi, it's the opposite. Kakashi views the world in a hopelessly pessimistic light. To him, everything is meaningless, senseless, and purposeless, a world full of actions that are futile and fruitless. One might not even try if such efforts will only come to nothing in the end.

Sasuke would rather passionately throw himself towards any goal or cause he believed in, no matter how implausible or impossible such a goal might be. Kakashi would rather avoid doing anything that doesn't seem doable or achievable and will generally only attempt things within his reach.

In this sense, they are opposites: Sasuke has an unhealthy obsession with his purpose, and Kakashi has an unhealthy obsession with his futility. Sasuke has an obsessive, over-focused fixation on relentlessly pursuing his life's purpose no matter the cost, and Kakashi is so aimless and unmotivated that no matter how bad things are, he can't be bothered to change his ways to make things better or prevent a growing crisis, no matter what his apathy is costing others.

Sasuke and Kakashi don't share much in common at all, and I want to dispel the myth that they are "alike", because they aren't. Their values and outlooks aren't very congruent or compatible with each other. They're closer to opposites in a lot of ways, maybe in just about every aspect. 

Kakashi and Sasuke value very different things and their personalities diverge so widely that Kakashi finds Sasuke unrelatable, and conversely, Sasuke finds Kakashi unrelatable, and neither one understands the other very well, if at all.