I will explain Brahma-Saṁhitā’s answer to this question, which accords with Śrī Bhāgavata Purāṇa, Bhagavad-Gītā, et.al. .

Hari

“Hari” is the the Onotologically Original Consciousnss Person. He is “ātma-rāma” (self-delighting)

Ramā

“Ramā” (not “rāma”) is his śakti, by which he actuates and enjoys his self-delight.

He is 100% absorbed in play with her, and 0% involved in anything else. All his limitless other powers are 100% focused on augmenting their delightful play.

Almost all…

Jīva

This play between Hari and Ramā is, essentially, what we identify as “love.” Love can never be mandatory, so it is not mandatory that all of Hari’s śakti particpate with this play. Some of Hari’s śakti may not be inclined to participate in it.

“Jīva” is what we will call them – the conscious entities who are inherently not inclined to participate in Hari’s play.

Prakṛti

The first problem the Jīva pose is that they have no place to exist, since all of existence is involved in Hari’s play. Hari solves the problem by setting aside a portion of his primary śakti (Ramā) for them to manifest their existence in.

“Prakṛti” is a shortened name for this set-aside śakti. Her full name is Aparā-Prakṛti (Subordinate Prakṛti), distinguishing her from her original form, Ramā, who is described as Parā-Prakṛti (Superior Prakṛti).

Śambhu

The next problem is how to put the jīva into contact with prakṛti.

This is a problem because the jīva are part of Hari, but Hari is absorbed without interruption in intercourse with Ramā. Therefore, how will he intercourse with the separated portion of Ramā, prakṛti, to place the jīva in her?

To solve this problem he creates a “viśeṣa-aṅga” (a “specially separate limb”) of himself, who will intercourse with prakṛtī. This is “Śambhu.”

Śambhu means one who establishes (-bhu) benediction (śam-). The benediction is twofold: immediate and ultimate. The immediate benediction is to allow Jīvas to realize their existence by establishing contact between them and Prakṛti. The ultimate benediction is to free the Jīva from their disinclination to participate in Hari’s play. The ultimate benediction is facilitated by the immediate. In other words, allowing the Jīva to fully explore the realities of existence outside of Hari’s play, blesses them with them the chance to hear about that play, which can lead them to seek an alternative to their non-inclination towards it.

Yoni – Liṅgam – Bīja

Placing Jīva into Prakṛtī is exactly analog to conventional male/female procreation. Śambhu is the liṅga (male sex organ) and Prakṛti the yoni (female sex organ). Śambhu places Jīvas in prakṛti the same way a male injects sperm into a womb, for the egg. The word bīja (“seed”) therefore describes the emission of the Jīva into Prakṛti.

However, there is a third problem. The jīva-bīja is within Hari, not within Hari’s “specially distinct limb,” Śambhu.

Mahā Viṣṇu

To solve this problem, Hari manifests himself as Mahā Viṣṇu – “the ultimate permeator.” He appears, with the jīva-bīja within him as his intrinsic śakti, within Śambhu.

In terms of the sexual analog, Hari becomes the sperm-containing semen within the special male sex-organ that is Śambhu. Using Śambhu, he ejects himself into Prakṛti. This insemination begins her cosmic gestational evolution. This causes instances or “bubbles” of evolved prakṛti to emerge from Mahāviṣṇu’s pores into the ocean he floats in within prakṛti.

Garbhodakaśayī Viṣṇu

Each “bubble” of embryonic instances of prakṛti is what we might call a proto-universe. To bring jīva into contact with these, he expands into each one.

We call this expansion Garbhodakaśayī Viṣṇu. This means the Viṣṇu who lies (śayī) on the “ocean” (udaka) within the womb (garbha).

His presence in each bubble causes further gestational evolution, and prakṛti now becomes able to produce complex combinations of her fundamental atomic elements.

Param-Ātmā

Now, the “birth” of the jīva as individual “children” is possible. For this, Viṣṇu manifests a lotus form from his navel and emits the jīva individually into it.

A final problem, however, is that the Jīva cannot directly interact with prakṛti. Both the jīva and prakṛti are connected intrinsically to Hari, but they are not intrinsically connected to each other. Therefore they have no natural means of interacting with each other.

Viṣṇu solves this problem by expanding once more. As each Jīva activates and separates from its amalgamated state, Viṣṇu remains in direct contact with it, acting as the conduit between it and prakṛtī.

“Paramātmā” is our name for this aspect of Viṣṇu, He is inseparable from the Jīva (ātma), but superior to it (param) because he is the substrate of its very being.

Brahmā, Śiva, Viṣṇu

The first Jīva born from the cosmic lotus will play a unique role in helping all the rest of them be born and live out their lives. Viṣṇu empowers it to master Prakṛti’s quality of creativity (rajo-guṇa). This Jīva becomes known as Brahmā.

For the Jīvas to exist stably, the other two of Prakṛti’s primary qualities must also be regulated and superintended. Her quality of realness (sattva-guṇa) is already taken care of in this regard, simply by the presence of Viṣṇu in her proximity. Her quality of destruction, however, needs a superintendent, and for this an avatāra of Śambhu manifests from the frustrated creativity of Brahmā. This being is known as Rudra, or more commonly as Śiva.

Shiva vs Vishnu?

Any view can be supported:

1) “Śiva is superior to Viṣṇu”

This view is valid from a certain perspective, since Śiva is an aspect of Śambhu (Śambhu is sometimes addressed as “Sadā-Śiva”, the “eternal Śiva”). Śambhu is ontologically prior to the three Puruṣa avatāra known as Viṣṇu.

2) “Viṣṇu is superior to Śiva”

This view is also valid, and perhaps moreso, since it is valid from more perspectives.

Firstly, Viṣṇu is an aspect of Hari, and Hari is ontologically prior to Śambhu.

Secondly, Mahā Viṣṇu is ontologically prior to Rudra, who is the primordial form of Śiva.

Thirdly, Viṣṇu is the regulator of sattva. Rudra is the regulator of tamas. Sattva‘s importance is far superior to tamas, because tamas (destruction) is simply a modification of sattva (existence).

3) “Viṣṇu OR Śiva” is an uninformed phrase. “Viṣṇu AND Śiva” is the informed phrase.

Since Śambhu Sadāśiva is the Viśeṣāga of Viṣṇu, it is rather artificial to separate the two as if they were separate beings who could be in competition. In other words although it does seem objectively demonstrable that Viṣṇu is superior to Śiva in more ways than not, it is odd to take the “who is superior?” question too seriously, since one is inside the other.