The fight of Lord Shiva and Lord Vishnu

In eternal believes there is three divide of supreme which called trinity god. they are Lord Brahma, Lord Vishnu, Lord Shiva. they are not a different they are same god, the name of God as work creator, preserver, and destroyer.
there is in Shiva Purana and Vishnu Purana two times fight between Lord Shiva and Lord Vishnu.


according to Shiva Purana, after the death of Sati(first wife of Shiva),
Lord Shiva left his duty(regeneration of universe). after that there was unbalance in-universe cause there was not destroying anything,
so that lord Vishnu prepared his plan that, he faced the fight with Lord Shiva then Lord Shiva can accept his trinity god duty, then lord Vishnu orders his vehicle(Garuda) to kill all of the snakes on earth.
after that Garuda, start to kill the all snake in the earth, in this time Vasuki(king of snake) going to Kailash for visit with Lord Shiva.
then garuda visit with Vasuki, garuda attack Vasuki and started fighting,

because of lord Brahma boon to Garuda, he is easily won Vasuki,

then garuda tries to kill Vasuki and Vasuki worship Lord Shiva and call for help,
then Lord Shiva came and order to garuda escape him, but Garuda said I am doing of the order lord Vishnu, so if he escape him, this is insult of Lord Vishnu, so I can't escape him, then lord Shiva get angry and going to kill Garuda, then garuda ask for help to Lord Vishnu. then lord Vishnu came,
and Lord Shiva and Lord Vishnu facing each other, Lord Shiva told that the order of killing all snake is wrong. there are equal rights for the snake. lord Vishnu answer that this the boon of Trinity, we must follow this, for the save Vasuki you need to kill garuda and for the kill Garuda, you need to defeat me first, then lord Vishnu challenge lord Shiva.
then whats after Lord Shiva get angry and lord Vishnu attack with gada(bludgeon) to Lord Shiva. but this disappeared when its near in Lord Shiva, then lord Shiva attack of Lord Vishnu hearts with Trishul(trident). then get the attack in heart, then lord Shiva weeps because in Vishnu's heart there lives lord Shiva, so Lord Shiva realizes that Trinity is same, then Lord Vishnu said your pain is my pain its all universe pain. so thatlord Shiva accept his duty. and he takes Vasuki(king of snake) as garland, and Lord Shiva is also known as Nagendra haraya.

So neither Lord shiva can defeat Lord Vishnu nor Lord Vishnu defeat Lord Shiva.

No one Can defeat Lord Shiva and No one can defeat Lord Vishnu.

Because 

SHIVAYA VISHNU ROOPAYA SHIVA ROOPAAYA VISHNAVE. SHIVASYA HRUDAYAM VISHNU VISHNOSCHA HRUDAYAGUM SHIVAH. YATHAA SHIVAMAYO VISHNU EVAM VISHNU MAYA SHIVAH
"shiva is form of vishnu, vishnu is in the form of shiva. shivas heart is vishnu, vishnus heart is shiva. however vishnu is full of shiva, same shiva is vishnus formed."
 

Thank you.