RoP: Infernal p31
Art and Academe p31
These passages certainly appear to be in contradiction
I like the RoP: Infernal take for game purposes, my villains are going to be run by me and they'll have my brain behind them. I also like the fact that the PC's can be smarter than any of the demons.
Are there metaphysics arguments one way o the other? historical arguments? other game play arguments?
From a pure gameplay standpoint (because I know not a thing about the metaphysics, theology or history of demons), I think the notion of pure intelligence could make demons very interesting adversaries. Here is foe who knows, at a glance, how the world works, how things fit together and so has a fair guess how to manipulate those things.
From a pure game standpoint, demons know the rules, know everyone stats, the best possible builds and how to manipulate the game to their advantage... rules-lawyers from hell as adversaries. 
Seriously though, it makes them the consumate schemers, the perfect deceivers and the guys who can offer you the path to ultimate power. Sounds good (well, evil) to me.
... Except that, without the virtue of Patience, they can't actually scheme very well (Serf's Parma ... unless they spend something... Might maybe? I don't remember. It's noted in RoP:I). This makes a lot of sense to me, and helped me define the difference between weak demons and powerful demons. Weak demons are just vice incarnate. Powerful demons have the ability to subdue their vices and strategize. Much nastier....
But to get back to Tyrell's question, while they're technically very opposing statements, I can see how they both could be used. If a demon can sense something, it gains complete understanding. With that understanding, it can reason itself to even greater understanding (of things beyond it's senses.)
Of course, I'm just talking out my behind here, having no formal knowledge of the subject.
Personally, I like the idea that Angels have "intelligentia", but Demons lost the ability during the Fall. It makes more metaphysical sense to me.
I like the RoP:Infernal take too. It seems to work better if they are to be actual opponents in-game of magi.
Also, as firth5 says demons are also meant to be without virtue --- for demons to exist in a state of perfect understanding seems wrong. Perfect understanding seems like a virtue, just being clever is not.
So, I think that demons can probably remember having a state of perfect understanding (pre-Fall), and individual demons might be significantly more intelligent than a man. Others are likely very stupid.
Doesn't intelligence have some nonobvious to the modern ear definition in A&A whereas RoP: I would use the more modern definition since it came out first?
My impressions after reading the book:
Only powerful demons can use confidence to reason to think something through, connect the part of their mind with memory to come up with a better course of action, or feign emotion. So they aren't the perfect liars after all, even if no magical means of discerning the truth works, their lies are not believable. They can't keep track of a lie, they cant remember what they said to whom or reason to change a lie to incorporate something, because they don't think its possible they will get caught. You also can't tell if they are telling the truth, indeed its my understanding that they can't pretend to have human emotions, so they can't be convincing when they act "surprised", "insulted", or "caring". So a Folk Ken roll will always show they are not displaying a proper emotion, so its safe to assume they are lying all the time.
They are seriously gullible too. If a trick works once, it will work all the time on the same demon. If a demon's 'plan' fails, it wasn't it's fault, it will do the same thing again and again. So they are easily manipulated or impossible to deal with, since they never learn from mistakes. They are rabid dogs with the memory of a gold fish. A powerful one could blow through a bunch of confidence in a scene and be a scheming devil from literature, but after that scene will go back to being a goldfish.
They lack the ability to negotiate or make realistic deals, so the only people that bargain with them are desperate beyond hope. No memory, no compassion, inability to be "fair".
In a lot of ways they act like monsters in movies.
In a fight, they don't go for the magic item, the book of incantations, the "whatever it is that will destroy them" but instead continue to try and kill, maim, torture, whom ever is currently in front of them. Pure mindless evil. I will only use them in this capacity. Otherwise my players will get annoyed at the fact that xyz Fairy or Daimon is really a demon and they can't do anything other that get npcs to solve the plot for them.
Otherwise my players will become disenfranchised:
"Here lets play a game that I have repeatedly told you has the best magic system ever, loosely based on the philosophy of Aristotle and Plato, it will be great. Sympathetic magic, fairies, Magical beings galore. Your enemy, you cant detect it. The only thing that can defeat it is npcs you can't affect."