But Visigothic Kingdom of Spain survived. Unlike Vandals - and unlike Ostrogoths.
It survived because, for once, Byzantines had a pretty much defined objective in the region, namely preventing Goths to be able to threaten conquered Africa; while Africa and Italy were considered to be taken over entierely and imperial order (or, rather, a certain idea of imperial order) restored.
Visigothic Spain (Roger Collins)
Once established in Spain, the Visigothic kingdom was far more secure than it had been under Alaric II, not least in terms of its much smaller and more mountainous borders, but the opportunities for conquest and expansion became almost nonexistent, especially after the Gothic forces were expelled from Ceuta and the North African coast in the time of Theudis, and then when parts of the peninsula itself were lost to the empire from 551 onward. The kings had less with which to reward faithful service, and their value to the regional aristocracies, competing for local status and authority, was consequently much reduced. [...]
The extinction of the "Balt" dynasty of Alaric I in 531 transformed the transmission of royal authority within the kingdom. Election of the king became a reality and dynastic sentiment was thereafter never a strong force in securing the easy transmission of power from father to son. Only a degree of inertia, whereby those already benefiting from the current ruling house would be disinclined for change for fear of losing their gains from a redistribution of royal patronage, favored dynastic continuity
It have really little to do with institutions, that can be considered being actually weaker in Gothic Spain than they were in Vandalic Africa or Gothic Italy, with a predominance of local authority. Gothic Spain was more strategically secure (by virtue of being more remote), but the kingdom wasn't stronger.
Romans attack, but after initial Roman victories Vandals drag out a war of attrition, and eventually Romans win a pyrrhic victory. As happened to Ostrogoths
The difference is that Vandals didn't benefit from a relatively long hinterland to withdraw and come back from, since Berbers ousted them from a lot of places at this point. You did had Vandals, Berbers and mutinees from the Roman army banding up soon after the conquest, but that's quite different from what was possible in Italy.
Romans attack, the Vandals drag out the war of attrition and eventually win the pyrrhic victory
Not only they can't really put a war of attrition if raided from the hinterland, but Constantinople is definitely able to sustain a war of attrition by itself as it prooved IOTL in Italy and Africa (essentially against Berbers). That it could be long and destructive was a secondary concern for them.
Better institutions (as in, keeping up the alliance with Mauri after 480s and converting them to Arianism rather than Niceanism)
Berber hostility after 480 is not a matter of "better institutiions" (Vandal approach being roughly the same than Romans before them), but a consequence of Vandalic policies and struggle against Nicean church.
As for conversion of Berbers to Homoeanism (rather than Arianism strictly speaking), there's a series of obstacles : forced conversions or even sponsored conversion were a relative rarity in Barbarian kingdoms, even in Africa. The whole point of battling Nicean clergy was less to impose Homoeanism to the whole population, than to deal with a particularily powerful church in Africa, something that was gradually toned down.
As for converting Berbers, there was no much reason to do that, as until the 480's and their gradual conversion to Nicean Christianity, it was quite fine : the lack of proselytism among pagan Barbarians by Homoeans is a general feature., which is arguably quite different in Africa with an existing (but not really applied, especially after Huneric) policy of converting local population to a same religious branch.
Missionary policies, either at sword point or just very proselyte, didn't became a feature before the middle VIIth century, and really present only in the VIIIth onward. The prime idea before, and in all Romania western as eastern, was to focus on the religious unity (which, at the partial exception of Vandals, didn't meant the disappearance of various branches in itself, but their fusion) within the states.
Trying to convert Berbers would be a radical departure, possibly requesting their earlier integration into Vandalic kingdom by sword point, which wouldn't be obviously successful, to say the least; and might require an earlier PoD in late Roman era to have this departure from IOTL policies being considered.
EDIT : the reason of the strong mutual hostility of African clergy and Vandals are rather complex, but could be summarized on some points.
- Genseric seems to have been a ruler with a strong political perspective, in a "cease or desist" ruthless attitude. Land confiscations in
sors wandalorum being made at the benefit of vandal subjects, the local clergy had to be purged at the benefit of vandalic clergy too.
- African clergy might have been strongly influenced by Donatism's puritanism and intransigence, not giving much to deal with, in spite of regular detentes in royal policy, especially knowing that they would be supported by Constantinople.
That led to a "holier than thou" attitude that was backed with full political power, leading to events considered aberrants in the light of Barbarian religious policy elsewhere.
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It could be butterflied with a Genseric with a less ruthless and visional out; or with Huneric keeping a fairly tolerant policy as he did initially, but note that Gothic tolerant religious policy in Italy didn't saved them from Justinian's expansionist policies; so maybe these kings weren't totally in the wrong thinking that, if you had to pull your weight, you could do so all the way for what it mattered.