Here is my answer which is based on the Devi Bhagavatam & the Vyasa Smriti.
The Devi Bhagavatam states that in such situations the views of the Puranas are to be rejected .In other words,the Smritis are more authoritative.
From Book 11,Chapter 1,Devi BhagavatamBook 11,Chapter 1,Devi Bhagavatam:
Nârada said :-- O Bhagavân! O Thou, the Eternal One! O Nârâyana! O Lord of the past and the future! Thou art the Creator and the Lord of all the beings that lived in the past and that will come into existence in the future.
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This is the advice of Manu.
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Nârada said :--– “O Muni! The S’âstras are not one, they are many and they they lay down different rules and contradictory opinions, How then Dharma Dharma is to be followed? And according what Dharma S’âstra?” Nârâyana said said :--– S’ruti and Smriti are the two eyes of God; the Purânam is His Heart Heart. Whatever is stated in S’ruti, the Smriti and the Purânams is Dharma; Dharma; whatever else is written in other S’âstras is not Dharma. Where Where you will find differences between S’ruti, Smriti and Purânas, accept accept the words of the S’rutis as final proofs. Wherever Smriti disagrees disagrees with the Purânas, know the Smritis more authoritative..
And where differences will crop up in the S’rutis themselves, know that that Dharma, too, is of two kinds. And And where the differences will crop up in the Smritis themselves, consider consider, then, that different things are aimed at. In some Purânas, the Dharma of the Tantras is duly described; but of these, which go against the Vedas, they are not to be accepted any means
Narayana is the eternal deity, however, he is using the advice of Manu Note that, rather than necessarily his own opinionhere Narayana refers to Rishi Narayana and not Lord Vishnu. Manu is a controversial figureNarada , so this depends on how much you trust himof course, is Deva Rishi Narada.
EDIT-In his speech here (which is a part of the book named "Hindu Dharma") Sri Chandrasekharendra Saraswathi MahaSwamiji also hints that as far as authority is concerned Sruti-Smriti-Purana is the usual order.So,Smritis are indeed considered as more authoritative than the Puranas.
But of course what he is actually trying to convey is that all the three has to be treated with equal importance as having same authority.
Those who composed the Smritis and laid down the performance of such rites must have been fully aware of the spirit of the Vedas. It is not proper to think that the Smritis are inferior to the Vedas or that the Puranas are inferior to the Smritis. We must learn to take an integrated view of all of them
The Vyasa Smriti also repeats the same thing which is said in the Devi Bhagavatam :
In matters of discrepancy between the S'rutis, Smrit'is, and Puranas, the former should be held as decisive, whereas the Smritis should have preference in all topics where there would be a difference of opinion between them and the Puranas.
Vyasa Smriti,Chapter 1,Verse 4.
So,the Smritis are indeed more authoritative than the Puranas.