Was Shiva created by Vishnu? Or Vishnu was Created by Lord Shiva?

The answer depends upon the philosophy you want to believe on

1.>Advaita
2.>Vaishnav
3.>Shaivism or Shaktism
 4.> ...

Shiva birth is only one with no gotra/lineage. He is an standalone entity in any sacred text so, he is ultimate one.

But his status is not equal than to that of Vishnu in eyes of human. Vishnu is responsible one who protects and is with people in disguise.(for instance king is considered as vishnu avatar). On the other hand Shiva has his own lifestyle, and is generally epicted as careless one who gives boon to anyone and can do anything(exotic dances, smoke, eat anything).No rules apply to him but he only respect nature/shakti rules so abide them. Even his lingas are worshipped by vishnu,indra and brahma.(Ref of worship for instance is in a story of deer where 3 pieces of deer horn are placed as lingas in 3 world by each above god.for eg brahma at gokarna.)

so it depends upon how you visualise trinity.

When there was a complete zero - the very beginning of the universe, Lord Vishnu was born from energy. Then from his navel a flower was born and Lord Brahma was sitting on it.

After their birth Lord Brahma introduced himself to lord Vishnu and greeted him and said - "I was pleased to meet someone after so many years of wandering". By saying that he claimed that he was the first to born.

Soon they both started arguing about who is the supreme noble among them. As the argument heated up an enormous black stone appeared and asks them to reach the ultimate end of that stone. Lord Brahma goes upward and lord Vishnu downwards.

They kept going - finally lord Vishnu realized that this stone (or lingam) is infinite like knowledge, it has no end so he returned.

But on the upper side lord Brahma kept going on, in his way he met a flower Ketki. And asked Ketki to claim that he bring Ketki from the end of that lingam. Lord Brahma reached the initial point with Ketki flower in his hand and told his false story to lord Vishnu. Soon a heavy furious voice echoed and Lord Shiva emerge in front. He was angry on Lord Brahma and cursed him that he will never be worshiped.

So according to this story Lord Shiva is most supreme of them all.

Being a vaishnava i would like to share based on whatever i have read.

there are 2 things:

1. nava vidha bhakti (9 types of devotion)
2. nava vidha dvesha(hating the lord in 9 ways)

Nava vidha Bhakti:

1. Shravanam - Listening.
2. Kirtanam - Singing .
3. Vishnu Smaranam - Thinking of God day and night .
4. Pada sevanam - Servitude to the feet of the Guru/God .
5. Archanam - Adoring the beauty of God .
6. Vandanam - Worshipping God .
7. Dasyam - Having the attitude of a servant to His master.
8. Sakhyam - Having the attitude of a friend toward God.
9. Atma Nivedhanam - Complete self-surrender toward God.

Nava vidha Dvesha:

1. Abhedha- believing that jeeva and paramatma are same

2. Nirgunatva - believing that lord does not have any kind of qualities.

3. apoornatva -thinking that lord is incomplete in all perspective

4. jiva-para saamya - thinking that jeeva and paramatma are equal

5. shrestatva -thinking that jeevas are greater than lord

6 . believing in svagata bedha(i.e finding differences in his activities) in lord himself

7. doubting the incarnation of lord

8. hating devotees of lord

9. vishnu shastra ninda- disagree with scriptures which praise lord vishnu’s glory.

Even if we do bhakti of lord along with the dvesha which are mentioned above , then bhakti is of no use.

So if we consider lord vishnu and shiva are equal, then it will come under one of the dvesha mentioned above.

We have to understand basic theory of hinduism for these types of questions. 
The basic theory of Hinduism resides in VEDANTA. Vedanta means the end of Veda. According to Vedanta,
                    There is only one GOD.
                    There is nothing except God in this world.
Maya (the illusion) that does exist itself, creates illusion of many existed.
Whatever we perceive through all senses, is all not true. There is no form of God OR We can say all forms are originated from one GOD. Form of Vishnu, Shiva or any other form of God, form of world, form of many people, anything whichever existed is GOD itself.

Shiva, Vishnu,Jesus or any name you can give. All are same.

Only saivism told like that. God understood by a person in very high end can understand that He can be called by any name.
So  not only Shiva and Vishnu are same , all God is same.

The necessary and sufficient answer is that Vaishnava texte will say that all manifested from Vishnu and Shaiva texts will say that all manifested from Shiva.

Yes lord vishnu created shiva but he is Not equal To him. who told you that shiva is equal to vishnu? even goddess lakshmi is Not equal to him. everyone is post shiva is post, indra is post, brahma is post every god is post but vishnu is not post. except lakshmi and vishnu everyone is post. all the devatas are devotees of vishnu. Hanuman, garuda, ahalya, prahalada,adi shesha, draupadi, Narada, indra, all These devatas are Big devotees of lord vishnu. we are living in earth because of vishnu. in varaha avtar vishnu killed hiranyaksha and he saved The earth. so only vishnu is supreme god No one is equal To him.

Yes in some scriptures vishnu created shiva.in others he did not.they are considered equals because both of them have vast followers who consider them the supreme form