The two texts are clearly addressing different types of themes and audiences. But is there a doctrinal difference, or just a difference in emphasis?
First, we can look to the might MN 43 and read:
āFeeling, perception, and consciousnessāthese things are mixed, not separate. And you can never completely dissect them so as to describe the difference between them.ā
But we may not be satisfied if we think that it is a generalization or a less authoritative statement when it comes to these two texts. Where else can we look then?
Well, we know that in the PÄrÄyanavagga, the whole point is about brahmins wanting to be free from nÄmarÅ«pa. The normal way to do this is to free the Ätman ā say, a sheer mass of consciousness ā out of nÄmarÅ«pa leaving only eternal bliss outside of the manifest world; brahman.
What the Buddha discovered is that nÄmarÅ«pa and viƱƱÄna mutually condition one another. The freedom from nÄmarÅ«pa, its cessation, is only to be found in the cessation of its condition: consciousness. So to these brahmins and contemplatives in the audience of the PÄrÄyana, this is the right material to offer them. It is also consistent with the Buddhaās teachings on causality found in every tradition of early Buddhism, all over the nikÄyas/Ägamas. In fact, the mutual conditionality between nÄmarÅ«pa and viƱƱÄna seems to perhaps be an older version of dependent origination that is directly connected to or associated with the Buddhaās awakening in some way.
What do I mean? In the standard story, the Buddha realized all 12 links. But interestingly enough, at SN 12.65, the Buddha gives an autobiography of his practice to awakening. Note that this sutta is actually put on the lips of the Buddha, whereas the story of e.g. Ud 1.1-3 is just narrated by someone else. Here, the Buddha says he realized the mutual conditionality and that was his key insight.
At DN 14, a neat little easter egg is hiding in the story about VipassÄ« Buddha: He too based his core insight on the mutual conditionality between name-&-form and consciousness! Why would tradition specify this chain? Well, we know that the Past Buddhas are all meant to follow the same patterns as our Buddha, with two chief disciples of the same type, etc. etc. in a cosmic universe. So it seems they are pointing to something they knew about the Buddhaās awakening.
Briefly, we can note that this is how the Buddha presents the complex theme of dependent origination at DN 15 ā the longest discourse on the subject in the canon, with several parallels, all sharing this feature. Namely, the explanation culminating in the mutual conditionality between name-&-form and consciousness. Note too that in some parallels, such as DA 13 I believe, there are layers to the text: in the introduction, they added a reference to āthese 12 dependent arisingā for the standard 12 links, and yet the actual sutta only explains the normal 9! So tradition recognized this lack, and in some cases tried to level it out later on. We also have outside discussions of it such as at SN 12.67, and at MN 38 ā the other long explanation of dependent arising ā the Buddha starts his actual, every-day example of dependent origination with consciousness and name-&-form.
Of course, even in the standard 12 links shared in every tradition, consciousness is conditioned and in relationship to name-&-form. So not only is this an extremely prevalent, common, and core essential doctrine of Early Buddhism, but it is also explicitly put on the lips of the Buddha and in the stories of past Buddhas several times in significant scenarios.
But wait, thereās more! We know that this question of the cessation of name-&-form as well as consciousness is extremely important to the contemplative Brahmanical groups of the time. We have confirmation of this outside the Buddhist texts in the BrÄhmanas and Upanisads by the way continuing for centuries. But we also know that these contemplatives were doing practices that the Buddha himself is also recorded as having done! The PÄrÄyana talks about the attainment of nothingness several times, precisely what the bodhisatta practiced before his awakening under apparently contemplative Brahmanical-based teachers!
The point is this: the teachings of the PÄrÄyana are confirmed time and again, from independent sources, internal and external, up the wazoo in the Early Texts. Itās actually astonishing.
So what about the cessation of perception? Well, DN 9 is a good place to start. Here we learn that there were a bunch of contemplatives, ascetics, and religious philosophers of the time with all kinds of different opinions on perception. It was an important subject ā the refinement, the limits, the happiness or suffering to be found in saĆ±Ć±Ä (perception). Indeed, when we look at Early Buddhist meditation and contemplation practices, they are also all about perception.
Perceiving impermanence, anattÄ, dukkha, asubha; perceiving the breath; perceiving earth, forest, the elements, space, the immaterial attainments. Even at DN 15, a text linked to the teachings of the PÄrÄyana and strikingly similar to Snp 4.11 ā in the Atthakavagga!! Seriously, compare Snp 4.11 to DN 15 ā we see that there are a class of ānon-percepient beingsā associated with the 4th jhÄna, and there is a refinement of perception up to the cessation of perception and feeling.
At DN 9, the golden sutta on perception, it too leads to the cessation of perception and feeling. This speaks nothing of consciousness/name-&-form, and yet it goes to the same place: the cessation of all experience, which, if one does not grasp to anything afterwards, is equivalent to nibbÄna and the same goal as the cessation of consciousness.
We can see that the practices and topics of the Atthakavagga are associated with general sramanas and contemplatives. Different experimental practices and observances (sÄ«la/vata), different views, different ideas on perception, notions of purity, debates and arguments. These are classic descriptions of the contemplative scene of the day and we see in the Atthakavagga a text that talks about navigating this scene. The PÄrÄyana addresses the other half of the story: Brahmanical philosophy that adapted itself into salvific and metaphysical thought. All throughout the discourses, we see the Buddha is a mastermind in managing both of these camps in very detailed, nuanced ways. It is not contradictory or mutually exclusive.
So when talking to contemplatives interested in perception, the Buddha did so. When talking to those interested in consciousness, he did so. He used some of their own terminology and worked with it in both cases, and yet ended up at the same place. Not only that, but the ideas are consistent with the heartwood of Early Buddhism found elsewhere, and we even see overlap between these approaches at DN 15. Perception, views, and contact are all related in EB discourse. And yet the cessation of contact/perception ends up being the same as the cessation of consciousness. The needs of the audience and subject matter seem to call for different teachings, but on closer inspection, they culminate in the same place.
None of this is to even mention that Snp 4 is all about the types of grasping (upÄdÄna) and how it leads to entanglement in the world ā rebirth. So many of the texts in the Atthakavagga talk about ending rebirth by not being established anywhere in perceptions, which means the cessation / non-planting of consciousness. The non-establishment and involvement of consciousness in the other aggregates is a major theme, if not the major theme, of Buddhism itself, summarized in the four noble truths.
Thereās a lot to say on this, but I think this is sufficient. The post has gotten quite long. People have been making all kinds of claims about the Atthakavagga ever since the West got a hold of it it seems. Most of them are just wishful thinking. I really appreciate your interest and enthusiasm in looking into this topic more! 
MettÄ