Yet this is never really played out in the books. We don't ever see the Reds in this light, they are more like Homeland Security than Police IMO ... they are incredibly specialized and the only times we really see the Reds response mechanism it's fairly militant. Both Galina and Toviene approach their job as a "mission". Perhaps Pevara expected a more LEO organization out of the Red thus informing her ultimate decision.

Greens, while obviously military in their organization, seem to be vastly more prepared to root out communities of Dark friends. Not that we really see them do much either, but the Greens we do encounter are much more likely to be out in the world engaging in fighting the forces of the Dark One which would imply that they are more likely to sniff out DFs than a group of Reds who are singularly hunting for male channelers, who are not by definition aligned with the DO.

I suppose my issue with this reason for Pevara choosing Red is that it feels irrelevant to me. It's like someone deciding to join Homeland Security instead of the Army because their family was killed by gang violence. There doesn't appear to be any real direct correlation in the choice of one over the other. What did the Red offer her that the Green could not in terms of stopping DFs?

I would have found it much more believable if she had chosen the Blue over the Green because of this reason, the Blue seeks justice and have causes they support so this would have seemed somewhat natural. Or if she had chosen the Green over the Brown or perhaps the Red over the Grey. The only real reason a woman would choose the Red instead of the Green would be around male channeling. The two Ajah are remarkably similar in function, despite the dramatic differences in their personality types, which seems like a giant hurdle for Pevara and honestly a failure on the part of the Green to ensure she was aware of her opportunities to fight the shadow.

Sieran's choice seems much more logical as she appears to have chosen the Grey for reasons related to ambition rather than functional duty. this is a woman who wanted political power and saw the path to that through the Grey, but the obvious failings of the Red in broader Tower politics would have made her pause in that selection. Clearly she was suited to the Grey, but her personality was clearly more of the Red archetype. Pevara's choice was obviously something people were surprised by too. I think the Accepted are guided to an Ajah to the point that it's a shock when/if they go a different way for ANY reason.