As mentioned earlier, Perturabo was born with the innate knowledge of pretty much all practical and metaphysical sciences, which pretty much sets him apart from all of his brothers in that he had no "real" childhood, no trial and error period of learning. On
his first day he was debating (and dismissing) the nature of religion with his planet's wise men, and was master-crafting swords better than most smiths. You'd reckon being born knowing everything would stunt your emotional growth. Yes, other Primarchs like Angron, the Lion or Kurze got a pretty raw start but for better or worse they learned to adapt and rise to greatness (or infamy). Perturabo started off already being as good as he was going to get; though it would take time for his body to grow strong, his mind was already at its peak, and he had to spend decades on a shitty little backwater planet with no appreciable resources with which to build an empire the same way that
Guilliman or
Dorn did, all the while having to slap down naysayers telling him that his fantasies of advanced engineering and space travel were impossible.
As to his mind, if a comparison could be made, then he was probably just as intelligent as Guilliman, if not more so due to the seeming wide range of his capabilities. (Guilliman was renowned neither as philosopher, smith or artisan). As a military strategist Perturabo could plan a campaign from start to finish in his mind using the arithmetic of war; where Guilliman could orchestrate a flawless battle plan from the command center,
Perturabo would enact it himself by plugging straight into the data feeds and absorbing all the info at once, circumventing the chain of command and issuing orders directly to squads, taking direct control of gun turrets and mechanised units and plotting their firing trajectories, even taking over starship systems and running them himself.
Thus lies the problem: Perturabo is a general as much as
any player of Warhammer 40,000 is a "general": he
sees the battlefield in terms of units with stat blocks; every soldier can be
reduced to a number based on his armament or capability which would
factor in to his arithmetic of war. Even Guilliman recognised the
random nature of war and how small moments of heroism could change the flow of battle; other generals could trust their men to follow their orders to the best of their abilities and even exceed them from time to time and pull off something spectacular. On the other hand, in sincerely believing in his own superiority Perturabo would micromanage everything and instead remove the agency of his officers and men. His soldiers would never get their chance to succeed or fail on their own terms and were essentially reduced to minis on a tabletop. Which in turn would make his men paranoid, wondering if they would be thrown away into the grinder or be blamed for failure when they couldn't match Perturabo's expectations.
Additionally, one could make the argument that while he had a vast store of knowledge he knew how to use, Perturabo's other major flaw as a tactician was that he was unimaginative in anything other than his areas of expertise. Godlike with an artisan's inspiration when it came to matters of logistics, technology, siegecraft, and artillery, but too much of a stubborn and entitled martyr-manchild to
use different tactics as a situation demanded, even when he was underestimated; it would seem that he refused to adapt because he was completely convinced of the logical superiority of his own methods, and to change them would be to suggest they were incorrect or inferior. This stubbornness might even be engineered into his particular gene-seed, as the sloppy victories his Legion achieved in the decades leading up to his rediscovery were on the whole spoiled by their refusal to change gears and try something different.
To be fair, he certainly wasn't the
only Primarch who was a
one-trick-pony, and many of those specialties were likely engineered into them by the Emperor, but his attitude certainly didn't help matters, whether he was calling Corax a coward for suggesting a feint, or dismissing (
or worse) his men for suggesting that a war of attrition might not be the best play. He may know how to crack an orbital defence that stymied three separate Legions, and how to dispassionately, surgically exploit killboxes to tear apart his opponents, but his tendency to dig in and throw men and big guns at the problem without paying heed to the input and suggestions of others made him ill-suited for
mobile and
asymmetrical warfare unless he had already engineered a means to keep them in place. There's even a scene in 'Path of Heaven' when Horus (swole from Chaos gains but still decidedly in his right mind as Warmaster) opines to Mortarion that Perturabo would be a poor choice to send after the Khan, believing that the Scars would run rings around his fortresses and artillery emplacements.
So ultimately, he was an ultra-competent specialist you could count on to perform his functions (but little else) to masterful effect no matter the cost, his crowning achievement likely being the fact that despite the degradation of so much of the Traitors' leadership and organization, Perturabo nearly-singlehandedly kept the siege running and the guns blasting on the logistical, strategic, and tactical levels. But he either couldn't or wouldn't change his methods even if he was ever wrong-footed, and his stubborn superiority-inferiority-martyr complex meant that he would never, EVER hear constructive feedback as anything other than a personal attack from an inferior mind. The main reason he was even functioning as a member of Team Horus was because, as mentioned, following orders and doing his duty were big things to him; without those, he likely would have been as much of a team player as Angron.
As an unwelcome revelation to the Mechanicum, Perturabo was quite capable of understanding binary machine code even when blurted out in its lightning fast audible form (something that would otherwise not be possible without some form of implants) to the point that tech priests unfamiliar with Perturabo would not actually believe it and be in for a shock when they attempted to use it in his presence (yet another example of Perturabo being underestimated).
Of all the Primarchs, Perturabo is the most misused of all. He was the only person in the Imperium of Man with his
savant-esque technical expertise; he can read and write binary fluently by heart, he's a master mathematician and engineer, he programmed a new AI from scratch for a Warhound Scout Titan that he hand-built from the ground up, all things that the Mechanicum and greater Imperium are in dire need of constantly. Nobody, not
Magnus nor
Ferrus Manus or
Belisarius Cawl could compare with his technical mastery, which remains unparalleled to the current millennium. Instead of assigning this literal Primarch-savant to research and development so nobody would have to waste time and energy kissing a machine spirit's ass for hours on end just to do
something, the Emperor saw fit to just throw Pert at walls.
All things considered, the only siege battle Perturabo should have ever fought would be a campaign on the bowels of Mars to purge it of all Archeotech bullshit like the Men of Iron, then emerge as a genuine hero and receive the accolades and recognition he would rightly deserve. Then put him to task on unfucking Mars' broken-ass atmosphere so the planet can flourish again, followed by putting him to task on creating STCs for brand new weaponry and AI to completely overwrite all the shitty machine spirits that have no place in holding the Imperium back from
full-throttle badassery. Would it piss the Mechanicum off? Probably, but what right would they
really have to complain about innovation after the Omnissiah's son just fixed two of their planet's worst problems? If anything, it would endear the populace of Mars to the Emperor more than ever and give Perturabo a purpose bigger than walking an army into a meat grinder over and over.
But you can't have a grimdark story without enormous potential being wasted fucking everywhere, now can you? To make an omelette, you gotta break eggs.
Unknown to anyone else, Perturabo had always possessed a strange connection to the Eye of Terror-- for some reason, he could sense it from anywhere in the galaxy, and he became convinced that it was constantly watching and judging his every action. The resulting inferiority (superiority) complex wasn't really helped by the fact that when he tried ask others if they could see the Eye, they assumed he was hallucinating.
(Ironically, he was actually the one to give the Eye its current name-- before then, it was called Cygnus X-1.) Considering he become one of those chosen by Chaos, he may have been right in feeling off at the Eye of Terror.