Interesting question. I would say they both fill the arch-nemesis role depending on the story: when Death appears, he and the other Dark judges nearly always go after Dredd and/or Anderson specifically, and end up targeting this dimension so often because of them. Maybe, as you said, is Dredd's opposite, being a chaotic anarchist who kills for pleasure, compared to Dredd, who is the law and kills either in self-defence or when the law demands he do so.
If I remember rightly, at the end of Day of Chaos, Maybe escaped with the Dark Judges into the Cursed Earth, so maybe there's the possibility of a teamup?
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Not quite. Maybe has Fear, Fire, and Mortis trapped in bottles, and is saving them for the right time, but he's still in MC-1.
Way back in 1991, during "Wot I did during Necropolis", when Maybe broke out of jail, one of the Sister of Death noticed Maybe and gave him a pat on the head. I suspect he probably will join forces with Judge Death when the latter returns at the end of the year.
As to the OP, I would say that Maybe is the archnemesis. He's the opposite of Dredd in almost every way - where Dredd is lawful, Maybe is chaotic. Where Dredd has the resources of Justice Department to call upon, Maybe has to make use of whatever he can scrounge up. Where Dredd is violent and a deadly fighter, Maybe is quite weak, and has to rely on his own genius. Plus, there's a distinct emotional connection between the two of them - while Dredd naturally hates Death, that's impersonal, since Death is merely a particularly dangerous serial killer. Maybe, on the other hand, has gotten under Dredd's skin, so when they tangle, there's definitely a personal aspect for Dredd.
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That's actually a pretty good point. Judge Death often gets touted as Dredd's arch-nemesis, but looking at the evidence, that's probably mostly due to the writers always bringing him back for some reason (popular demand?): see Revenge in the Anderson strip, Necropolis, Day of Chaos and possibly even more as time goes on.
Speaking as a mostly foreigner to the Dredd franchise (I've watched the Stallone movie and read the first Batman crossover and the Predator one, but that's it), I always assumed Death was supposed to be the undoubtable archenemy. I heard of Death for years and years, but I never knew about PJ Maybe until like a year ago in this very same site.
Judge death is the closest to an archfoe Dredd has. Dredd doesn't have many recurrers and the few he did are dead (Orlok the assasain) or pensioned off (poor mean machine)
Maybe was a recurring pest until the last few years when he took a bigger role in the sinfeld business and eventually being mayor of mega city one. I still think deaths the main foe though
" I did the right thing, didn't I? It all worked out in the end." "In the end? Nothing ends, Adrian. Nothing ever ends."I just think it's interesting that how Death is widely recognized as Dredd's arch nemesis and yet some people consider Maybe to be that to Dredd. I even read somewhere on a website blurb in the search page that Orlok comes a close second to Death. Honestly the only Maybe story I read so far is the one where he kills off the Yess family and not even up to his capture yet. I was wondering if anyone knew where those kinds of moments between Maybe and Dredd have occurred with each other? I Guess it depends on the writer though that isn't to say that Death or Maybe doesn't have their merits. Really Maybe and Death are so different yet so similar kind of like a two sided coin.
@optimusjamie: It's also interesting to note that Judge Death appears more often inAnderson than he does in Dredd. I think he actually makes a good archnemesis for Anderson, since his sadism, nihilism, and omnicidality conflict with her compassion and goodness on a much more intimate level.
@Napoleon: That is what Judge Death was created for. Since Dredd kills his enemies, either Tharg or Wagner and Grant felt he needed an adversary who could not die.
However, I feel that over time, PJ Maybe has taken on the role of Dredd's true archnemesis, partly due to the aforementioned emotional interactions between them, and partly because Maybe is human. Sure, Death was once, but he's ultimately an evil grim reaper, almost a force of nature more than a character.
That said, Death was much more active than Maybe during the 80s and early 90s, which was the golden age of 2000 AD. Plus, PJ Maybe hasn't led any epics (his biggest role was as one of several major players during "Tour of Duty"), while the Dark Judges were at the centre of "Necropolis", which spun out "Mechanismo" and had significant repercussions in "Judgement Day". This gave Judge Death the status of Dredd's highest-profile recurring enemy.
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Now that I think about it I read "Necropolis" and in that epic Death didn't even interact with Dredd most of the time if not the entire time. There was one moment where Mcgruder said that Dredd looks like Judge Death to which Dredd replies "Let's hope it's not an omen" and then Death just committed suicide (Well as close to suicide as he can get) by jumping from a great height near the end of it. I'm sure I read that "Judgement on Gotham" the Batman crossover followed Necropolis after Death's escape but I'm not sure.

I thought I'd ask you guys who would you consider out of these 2 to be Dredd's true Arch Nemesis? Both of them have pretty good chances with Death being Dredd's Evil Counterpart and Maybe being a major thorn in Dredd's side since he was 13 years old plus being Dredd's opposite.