Which rematch would be the most compelling for Anthony Joshua?

Yes, there is plenty on the road ahead for him looking forward instead of backward: mandatory defense vs. division bogeyman Alexander Povetkin, unification with Deontay Wilder, and freshfaced challenges from the likes of Jarrell Miller, Oscar Rivas or Kubrat Pulev (should he get past Breazeale in their eliminator), or any of the recent top challengers who came up short against his then-peers: Hughie Fury, Andy Ruiz Jr. or Luis Ortiz. Should none of those materialize, however, due to all the usual complications: boxing politics, failed negotiations, incompatible schedules, and the like - would not a rehash be preferable to dipping into the bottom of the barrel to waste a title defense on any yo-yo populating the HW division that isn't either named above in this paragraph, or below?

Here are the half dozen options, comprising all the currently or recently world ranked opponents Joshua has fought - and nearly the full balance of his workload in the last 2½ years (sans that fat useless bum Molina, against whom a rematch would be a ridiculously pointless exercise). They are listed in reverse chronological order that he fought them:

1. Joseph Parker II (Pros: they just fought on close terms in an important unification, to a draw on my scorecard. Lots of controversy about the wideness of the official cards if not the result, although some did have Parker winning. Even those scoring it for Joshua remarked they were surprised by Parker's skill and had expected him to be knocked out. First man to bring Joshua the distance. Cons: many - not I, but many - claimed it was "boring". They very likely would go another twelve, with more scorecard disagreement, lessening instead of enhancing clarity as to whom the better man was proven to be... Parker also was treading a fine line between sportsmanlike humility and being down on himself in the aftermath, so would probably need a win first as both confidence-builder and to not be challenging off a loss...)
   
2. Carlos Takam II (Pros: his performance on late notice was roundly praised, and Takam with a full camp perhaps could expand upon the discomfort he caused the champion in spots. Cons: has been pretty clearly beaten in his last two important fights, and stopped in two of his last three. Would be challenging off the loss...
   
3. Wladimir Klitschko II (Pros: it was a FOTY candidate last time, probably the shoe-in for heavyweight, and the rematch was actually supposed to happen and in negotiation for much of last year. Cons: the aging former HW king has already walked away from the game and flatly refuted any speculation as to his retirement being temporary, outside his April Fool's Day prank)
4. Dominic Breazeale II (Pros: assuming for the sake of argument in this scenario that he is coming off a victory over Kubrat Pulev, that will make for three fairly solid wins in a row...or at least two very good ones in Pulev and Ugonoh, plus a perfectly acceptable tuneup in Fatty Molina. Cons: he didn't win a round last time, and was beaten like a drum and stopped emphatically. He doesn't seem to have made any relevant improvements to his game since then, and never really hurt Joshua.
5. Charles Martin II (Pros: the general feeling was that all the bright lights and the big moment "got to" Martin, so perhaps the spectacle witnessed didn't give the best representation of how a fight between them might go if he had his head on straight. He went through a bit of a mental breakdown and some legal trouble afterward, but seemed to get on the straight & narrow last year and returned with a hunger, scoring two early knockouts to start working his way up the rankings again. Cons: it was a goddamn embarrassing KO2. First hard right hand taken, he rode an entire 9-count on a glove, knee and foot like a damn tripod, got up, immediately ate one more right hand and then rode a 9½ count and managed to have the gall to look shocked the ref waved it off. )
   
6. Dillian Whyte II (Pros: He is on a 7-0, 4 KO run since his loss to Joshua, with some good names in there and showing decent form. He also did have success in their previous encounter, and buzzed Joshua early...and still carries the psychological advantage of savaging him in the amateurs, which has now been once avenged but still just pulls Joshua level with him in the rivalry. Cons: Joshua had figured him all out by the midway point of their last match, and stopped him in pretty short order after that. Both are better than in 2015, but Joshua in greater measure, and styles will always favor him...)

 

I'd say:

1st tier: Parker or Klitschko. In that order. Both are underdogs in a rematch but not by anywhere near as much as the others. Parker gets first preference because he earned a draw on my card while Klitschko got stopped.

2nd tier: Whyte or Takam. In that order. Would be almost certain to be carbon-copies of their first times with Joshua, give or take. Maybe an improving Whyte or a full-camp Takam bags an extra round in the process, but most likely neither has the secret formula to beat AJ. Whyte preferable because he's on a lengthy win streak and his resume beats Takam's.

Bottom tier: Breazeale or Martin. In that order. These are the deep-sigh, "Yeah, okay, I suppose this is better than scraping the bottom of the barrel if fights against Wilder/Povetkin/T. Fury/Miller/Rivas/Pulev/H. Fury/Ruiz/Ortiz can't be made right now, for whatever reason..." This is the foul-tasting medicine you force down your throat, because a redundant session of dominating and knocking out Breazeale or Martin is probably better for the heavyweight division and better for Joshua himself than having the champ with three belts just sit on the shelf for an extended period. Breazeale is preferable because he lasted thrice as long as Martin and didn't fold at the first power shot; on the contrary he carried himself as far as he did on sheer chin.