What would happen if two Inquisitors accused each other of HERESY!

They would each seek to convince their peers; other Inquisitors working in same location and of the same Ordo. An Inquisitor Lord, who holds a lot of sway in the local (and by local, probably read "sector") Ordo Hereticus might be prevailed upon to render a judgement.

In the even of roughly equal support amongst their peers, they probably engage in shadow warfare, seeking to stop, capture or kill each other without making enough of a mess to alienate their peers.

The Ordo separates them to different Segmentums and tells them not to cross into each other's territory. Just like you'd put kids in different rooms if they didn't want to get along

>They manipulate other Inquisitors and other Imperial agents to try and attack the other's assets.

There will probably come a point where they become enough of a pain in the ass that a conclave of senior Inquisitors declare them both heretics. There would probably be investigation and warnings first.

But if neither can prove the other a heretic, neither has more friends than the other, seperating them isn't working and they will not stop fighting, eventually senior Inquisitors will deal with the problem forcibly, rather than let them consume Inquisitorial resources with their feuding.

Read Eisenhorn

>they probably send their teams to kill each other

Or, they will arbitrarily decide that one is a Heretic to save themselves extra effort.

While that's possible; remember, these are the inquisitor's peers and colleagues. They probably would at least try to do due process.

(After all, if they were accused of heresy one day by a secretly heretic inquisitor, they'd want their peers to look into the matter rather than write them both off)

Wouldn't it make more sense that both Inquisitors are put under scrutiny of Ordo Hereticus as a whole?

Like, I dunno, some Internal Affairs in the police type of deal?

In an ideal world, perhaps. But this isn't an ideal world; perhaps both Inquisitors have friends or have leverage over the local Hereticus in some way, or there's bigger problems for them to deal with, or there's factional play beyond simple Inquisitorial Ordos at play here.

THIS

Power and influence inherently can't be equal given the uniqueness of each inquisitor, the personal nature of their training and experience, contacts and connection established, factional allegiances, philosophical inclinations and doctrines, areas and modes of operation, etc.

>Thorian with navigation guild connections attempts to isolate and hinder the movements of his rival over decades causing them to appear lax and incompetent, cutting off resources and building a case to present where their rival will be lost in the warp during the proceedings.
>Monodominant admech supporter observes and collects data with cybernetic means from thousands of every-day surveillance devices, builds a strike team of psychically shielded combat servitors, waits for rival to be recorded in the act of something suspicious, or a number of correlated suspicious activities, secures a writ to arrest them, kills rival while pursuing them
>Recongregator with rogue trader and cultist connections through the subsector builds the influence and power of a cult that will be of obvious interest to their rival, plants heritical texts that the rival will confiscate and keep, tracks texts to rival and brings forward case of heresy

this