There must be lots of "Carthage Prevails?" threads somewhere, but I haven't seen them. From the responses I got to suggestions they could have done better in threads with different focuses--these being a long time ago when I was pretty new to the site in the early 2010s--it seemed a lot of people had the consensus idea that Carthage lacked depth that Rome had. Rome was a land power that used its expanding wealth to acquire a navy, but the Carthaginians were "just" a thalassocracy of sorts, if even that--they had really great breadth as sea traders with bases reaching up to Britain and down the northwest African coast, but apparently lacked the manpower to generally match expanded Roman capabilities. Sort of a Portugal versus Spain type situation.
Others also seemed to suggest that Roman society did a better job of engaging its elements, from common plebeians to oligarchic patricians, in the military-political business of expanding hegemony and empire--certainly around the time of Augustus and infamously the entire generation or three before, this was transitioning over, but in these classic days of Punic wars, the path of glory for an ambitious citizen of suitable rank harnessed the ambitions and fortunes of these favored and empowered competitors to public service, more or less; the implication was that Carthage by contrast was much more a straightforward oligarchy, already suffering from one of the diseases said to relate to the eventual fall of the Western Roman Empire the better part of a thousand years hence--the powerful and wealthy thought in terms of their profit and benefit and not in terms of the sort of glory and honor the Republican Romans emphasized; the wider masses, even those clearly elevated above servile rank, were not as engaged in the machinery and also apt to be looking to commercial and social status, not public service. Now I don't know how much weight to attach to these judgements, or if the naysayers about Carthage were even actually meaning to say something like this, but that is the impression they gave me.
(While I was sidetracked from finishing this post,
@cincpac overboard seems to have given an example of this general theory of inherent Punic doom in post 6--not that they said Carthage could not pull itself together, but that to do so would require some kind of drastic change in the nature of its society).
Thus, I suppose for Carthage to prevail over Rome, one of several things must happen:
0)--Carthage outlives Rome but some third power more or less takes Rome's place, or divides the potential power controlling the Western Med region could give a single hegemon in squabbling perhaps; Carthage is not really stronger than OTL but lasts until someone other than Rome slaps them down;
1) --Carthage prevails by luck or being a bit more proactive in breaking Roman power earlier, being more foresightful about the potential threat of Rome perhaps, and then having been taught a sobering lesson by a near run thing, perhaps reforms itself somehow to provide better what they allegedly lacked. Perhaps this is a matter of becoming a clever patron of many auxiliary allies that they manage to provide the manpower to go with their ubiquitous presence on the seas, or some deep reform raising up people who regard themselves as Carthaginian, say on spreading territory in North Africa analogous to Roman expansion over Italy, who also provide the necessary and capable manpower;
2) Carthage provides herself with peer allies, say having fostered a strong Iberian kingdom of some kind that views itself as symbiotic with Carthage, or a long standing alliance with Massalia or some other set of Greek city states, in Magna Graecia probably;
3) Carthage deviated from OTL long before the Romans started to cross swords with them, again supplying themselves via ATL alternate choices with what it was Rome had they supposedly lacked, so that this combined with their OTL sea power meant they were a century or three ahead of the Romans and managed to gradually defeat and tame the Latins, or of course effectively eradicate them.
1 and 3 seem to be the classic lazy AH trope of Carthage instead of Rome, and 3 seems to be asking that Carthage not be Carthage but be Carthage-Su-every advantage Carthage had OTL plus a good share of Roman advantages, which is probably too much to ask.
I'd explore the weirder variations on 1 and 2; the Carthaginians building an empire on a patchwork basis of nominally sovereign, autonomous small power allies in an eclectic quilt knit together by sea trade and some sort of more or less central council for a league that manages to avoid any of its component parts spinning off to wreck the structure with narrower ambitions. Or finding an ally and in effect negotiating the same sort of soft power hegemony but with fewer stronger players.
There was a TL going some years back about Massalia that might give a hook for a Carthaginian alliance with that ATL power crushing Rome and coming up perhaps with a federation, though I think the author there was going to have Massalia emerge triumphant in Rome's place, more or less, much as my Option 0 perhaps via a temporary option 2.
