I found the comparisons glaring.
Personality: both are bitter and angry at the unfairness of the world around them or, specifically, to them.
Motive: Admittedly different -- Adachi didn't have a motivation besides the power rush and the thrill of murder, while Akechi just wanted to get closer to his sociopathic father.
Method: both used the Shadow World/Metaverse to kill people.
Relationship with the protagonist: a twisted association originally based around lying to each other, before they both acknowledge that they have a lot in common and that their relationship with society is broken and unfair, with both choosing to react differently and to fight it in their own way.
This is such a reductionist view of both Adachi and Akechi's characters that it's physically painful to me.
Personality: That's not really either of their personalities. Adachi's more or less just an aloof dope who ran out of his final fuck to give years and years before the game's start. Akechi's a picture-perfect control freak who's very meticulous about every single little detail in his life. The bitterness is an aspect of both of them, sure, but it's not really what you see from them 99% of the time they're on screen. It's also much more prominent in Adachi than it is in Akechi. Adachi actively wanted to watch the world burn because he was so salty about his circumstances. It wasn't at all Akechi's primary goal -- he just wouldn't have been particularly pressed if it
did happen. This would be like saying that Yukiko and Haru have the same personality because they're both pretty rich girls who really don't want to take over the family business and feel lost at sea because of it. It's a very small part of who they are, though it's definitely a bigger part of Yukiko than it is Haru.
Motive: Oh, buddy. If you think Akechi's motive was to be closer with his dad, you missed the whole point of his character entirely.
Method: Disagree, and this is also super reductionist. Adachi couldn't even be assed to go into the TV world at all most times, and certainly not when he killed. He just lazily shoved girls in there and laughed about it. He was also never the one who actually killed them; he always waited for Shadows to do his dirty work for him. Akechi actively pursued each of his targets, sometimes battling through entire palaces to get there, and he was always the one who pulled the trigger.
Relationship with protagonist: Adachi never openly pursued Yu from a protagonist/antagonist perspective the way that Akechi pursued Joker. Adachi lied to Yu just to cover his own ass. Akechi lied to Joker with the explicit intention of betrayal, subterfuge, and murder. Akechi also genuinely liked Joker and resented the circumstances keeping them at odds with each other, whereas Adachi never really came around to Yu. Akechi wanted to
be Joker -- and short of that, wanted to be close to him, no matter what form it took. Adachi never, at any point, saw Yu as anything other than an annoying shitkid who needs to shut up, grow up, and get out of his face. Even after you beat Adachi, he's just like, "k you won, kill me so that I don't have to fucking dEAL WITH YOUR BULLSHIT ANYMORE."