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We know that if there is a conflict between the Vedas and smritis, Vedas has to be accepted. Similarly if there is a conflict between smritis and puranas,smritis have to be accepted. But what is the position of the Tantras? When does it win and when does it lose?

Upendra Kumar Das writes in the introduction of the KulArnava Tantram:

One thing we need to fix our mind upon here. Hindu Dharma has two ways -
the Vedic way and the Tantric way - and they are Swatantra
(independent of each other).

That means, while Vedamulak scriptures like Smritis and PurAnas derive the authority from the Vedas, Tantra's authority is independent.

Tantras' authority comes from the fact that they are "Shivavaktranirgatah" or "that comes from Shiva's mouth".

In Nitya Shodashika Arnava Tantram 1.13 Sri Devi says:

Sri Devi uvAcha:

Bhagavan sarva mantrAscha bhavatA me prakAshitAh |
Chatuh
shashtishcha tantrAni mAtrinA muttamAni tu ||

O Bhagavan, you have revealed to me the 64 Tantras comprising of all the
Mantras and some excellent Tantras related to the MAtrikas.

and, then she gives the names of the 64 Tantras and finally says:

EvametAni shAstrAni tathAnyAnyapi kotishah |
Bhava tokAni me deva
sarva gyAna mayAni cha ||

These all-knowledge-endowed Tantras you have revealed and similarly
crores and crores (i.e numerous) such other similar Tantras.

So, the authority of the Tantras come from the fact that they come from Lord Shiva's mouth.

On this verse, the Sri VidyA AchArya, BhAskara RAya quotes a verse which gives an etymology for the word "ShAstra" (which I have used in this answer) and says:

These 64 Tantras are Veda-like scriptures. They are the essence of the
Vedas. And besides that, since like the Vedas, Tantras come directly
from God's mouth (he uses the word - ShAkshAt BhagavadAgyA), Tantras'
authority can not be questioned.

And, the same thing is stated by Lord Shiva himself:

Mama pancha mukhebhyashcha panchAmnAyAh samudgatAh |
Purvashcha
pashchimas chaiva dakshinas cha uttaras tathA ||
UrdhAmnAyashcha
panchaite moksha mArgAh prakirtitAh ||

From my 5 faces emerged the 5 Amnayas. East, West, South, North and
High (Urdha) - These 5 Amanyas are known to be roads to liberation
(MokshamArga).

KulArnava Tantram 3.7

and, these Amnayas are the sources for the Tantras.

Another verse where Lord Shiva says that the authority of Tantras (although the verse is specific to Kula ShAstras but it can be generalized) can not be refuted simply because he himself has said them:

Kula shAstrAni sarvAni mayi boktAni pArvati |
PramAnAni na Sandeho
na hantavyAni hetubhihi ||

O PArvati, all Kula ShAstras are said by me. Therefore, all those are
without doubt authority and the authority can not be refuted by any
reasonings.

KulArnava Tantram 2.140

So, Tantras do not have a competition with the Smritis and PurAnas, because these 2 derive their authority from the Vedas, whereas Tantras has independent authority for the aforementioned reasons.

As you may know MahAnirvAna Tantram says Tantras are the mass of Agamas and Nigamas and once you see the definitions (etymological derivations) of those 2 words you will know why Tantras' authority can not be questioned:

Agama:

Agatah shivavaktrebhyo gatancha girijAsrutau matancha
vAsudevasya tasmAdagammuchyate||

That which comes from Shiva's mouth (that is spoken by Lord Shiva)
goes to GirijA's ears (that is heard by Goddess PArvati) and which is
approved by Vasudeva (that is Lord Vishnu) is called Agama.

Nigama:

Nirgatam girijAvaktrAd gatancha girishshrutau matancha vAsudevasya nigamah parikathyate ||

That which has emerged from the mouth of PArvati, goes to Shiva's ears
and is approved by VAsudeva is Nigama.