On the whole Henry vs. Peri thing, I think it comes down to how the story makes them enjoyable on top of how believable they come across.
With Henry, the thing is in his own twisted way, he does understand there are lines he shouldn't cross. He enjoys blood, but he's not going to go out and kill people for fun, he'll do it within the bounds of society and obey the rules people set for him. The character also benefitted from having good writing around him as the characters react justifiably to his actions, his supports are pretty good, and the character as mentioned before has a charm to his craziness, so it's much easier to tolerate him as he's an amoral character that doesn't stretch your suspension of disbelief too much due to having limits to his behavior and is genuinely enjoyable.
With Peri, the character isn't integrated into the cast and story well at all. As mentioned before, unlike Henry, she murders indiscriminately, will attack even allies (poor Felicia), and has no moral regard to others around her, yet we're supposed to believe she is hanging around characters that would otherwise shun those like her. She acts childishly and whines, which while it does fit into her backstory also makes her less enjoyable since bratty behavior is something that is not nearly as tolerated as Henry's oddities. Finally, she also has a nasty habit of making some characters bend over backwards to accommodate her behavior as you have things like Corrin saying "don't worry, I'll get you some sturdy guys to beat up when you get crazy" in their S support, Leo pretty much conceding to her after failing to explain why pointless murder is different from war when he's otherwise well spoken enough to explain things like that (which is strange as Laslow does it fine, but beside the point), and makes Xander look even more hypocritical then he already is in the story by employing a murderous womanchild despite also denouncing Hans for similar behavior. She does have a backstory, but off the top of the my head it only pops up once and it's not utilized enough to completely justify her behavior, so it ends up being an underdeveloped trait that doesn't fully salvage the character's worst behavior in her other supports. So that makes her hard to buy even when we understand how she grew up that way since they don't do enough with the backstory to make her more understandable nor make the other characters better understand her and try to help her, which makes her unlikeable on top of being unbelieveable.
In short, Henry worked because the character was written in a way that allowed him to be within enough moral bounds to work with the rest of the cast and had traits that made him likeable. Peri isn't done all that well in that regard as the cast doesn't react in a way that's believeable, doesn't work well with the story, and her childish behavior makes her even less likable. If they delved into the deep roots of her behavior more and wrote her supports with other characters more carefully, I think she would've been received at least a bit better, but her current state makes her hard to swallow and it's not hard to see why she's such a contested character among Serenes Forest and other FE fansites.