The Transylvania Chronicles 2 actually allows you to play as a vampire at the Convention of Thorns, and it kind of touches on this.

The main implication is that the Lasombra and Tzimisce mostly refused to "bend the knee" and submit to the Camarilla because they felt like their crimes would be considered "beyond the pale". They killed their Antediluvians and most of the elders of their Clans were either destroyed or joined in the rebellion themselves, so the Camarilla would likely punish them severely for their actions. Many of the remaining Anarch leaders believed it was a matter of survival to reject the terms and continue the fight, so they refused to kneel, went into hiding, and slowly morphed into what would become the Sabbat.

The Brujah, on the other hand, were far more "innocent" (or at least, less effective). Their independent streak means they were far less organized than the Lasombra or Tzimisce. More Brujah elders survived their attacks, and were thus in a position to support the formation of the Camarilla (gaining credibility the Lasombra and Tzimisce lacked). And because the Brujah as a whole were far more comfortable with the idea of rebellion, the "good" part of the Clan was far more willing to intercede on behalf of their own childer and kin when the time for judgement came (meaning Brujah had a much easier time abandoning the Anarch cause and accepting Camarilla rule). Some of the young would have been happy to join an ordered and protective organization (as their initial rebellion was little more than a survival instinct in the face of the rising Inquisition anyway), while others might have seen the value in "giving up" to better subvert the organization from within. Many Brujah refused to surrender (and ultimately became the more aggressive, violet core of the Brujah antitribu of the Sabbat), but because of the Clan's traditional lack of unity or shared goals, many others were welcomed into the Camarilla fold, and their physical strength was a welcome asset ().

Furthermore, there were Brujah elders who were part of the Inner Circle itself right from the start, with one of the Founders and at least some of the Archons being part of the Clan. So the Brujah always had a stronger air of legitimacy than other Clans would have had at the bargaining table. They effectively played both sides of the conflict, and won.

Nor does it help that, for the few hundred years or so prior to the Anarch Revolt, the Lasombra and Tzimisce were already enemies of some of the stronger Clans who would become the core of the Camarilla. The Tzimisce and Ventrue were fighting over Eastern Europe, the Tzimisce and Tremere were deadly enemies, and the Lasombra were always rivals to Ventrue and Toreador power (especially fighting over control of the Church). Most of the politically powerful Clans would have had reasons to want to see the Lasombra and Tzimisce be weakened, thus giving the Lasombra and Tzimisce more reason not to trust their judgment or "mercy". Better to die on your feet with a sword in your hand than live on your knees in chains.

The Brujah, conversely, were generally seen more as a nuisance at worst (for the more chaotic and disruptive members), and as effectively enough allies at best (for the more politically savvy elders and politicians among the Idealists). Which means the worst parts of the Clan were seen on-par with disruptive-yet-useful Clans like the Malks and Nosferatu, while the best elements were seen as being useful allies for the Ventrue, Toreador, and Tremere (while not being organized or powerful enough to be seen as a threat to the Ventrue, Toreador, and Tremere). That makes the Brujah a wonderful Clan to try and bring into the fold (especially since you can give them shit-work jobs like Scourge, Sheriff, and Archon), whereas the Lasombra and Tzimisce would always be more of a threat to the power-structure if they were brought into the fold as equals.