There is no difference between Narayana and Krishna. Both are the same. SriMadhvacharya, in the Mahabharata Tatparya Nirnaya, says that thinking there is a difference between Srihari and His avatars is a great sin and is one of the nine forms of hatred. And hatred in Bhagavan leads to Naraka, not Moksha.
110. The knowledge (belief) of non-difference between Paramatma and Jeevas; the knowledge of Paramatma having no attributes; the knowledge of Him having incomplete attributes; equating Paramatma with others; knowledge that others are higher than Him; knowledge of difference in His various forms and attributes and actions (contd)
111. The knowledge of birth and death for Him in His avatars; the hatred of His devotees; the condemnation of all those knowledge sources which proclaim His supremacy; knowledgeable people term these as the nine forms of hatred.
[Mahabharata Tatparya Nirnaya, Chapter 1, Sarva Shaastraartha Nirnaya]
Not only this, but the Puranas also tell the same.
यथा सर्वेश्वरो विष्णुः सर्वशक्तिसमन्वितः ।
तथैव तत्प्रभावाश्च अवतारा न संशयः ॥
Just as the Supreme Lord of all, Sri Vishnu, is completely endowed with all-pervading powers, exactly so are His glorious incarnations (avatāras). Of this, there is absolutely no doubt.
[Padma Purana]
Even in the Pancharaatra Aagamas, Lord Brahma praises Lord Vishnu as “नमस्तेस्तु नृसिंहादि मूर्त्यभेदाय विष्णवे,” which clearly tells that there is no difference between the avataras of Lord Vishnu and Lord Vishnu Himself. Be it in mood, be it in valor, be it in knowledge, be it in strength, be it in beauty, be it in opulence, be it in attributes, all avataras of Lord Vishnu are the same as Lord Vishnu Himself. The same Lord Vishnu incarnates on the earth. When Lord Vishnu incarnates on the earth, no earthly rules apply to Him. He acts as a human being to teach humanity to the humans and to delude the ignorant people.
Let me explain to you with an example. You have two lamps. You light both the lamps. Is the fire in those lamps different? No. Both are fire. We cannot say the fire in lamp 1 is superior to the fire in lamp 2. So, similarly, the Bhagavan is the same, be it Moola Roopi Narayana or Avataara roopa. There doesn’t exist any difference. In the Bhagavata, there comes an incident wherein a Brahmana’s sons go missing directly after birth. It escalates so much that Arjuna too couldn’t protect the Brahmana’s baby. Thus, Krishna and Arjuna have to go to Vaikuntha. There, Krishna enters Lord Ananta Padmanabha in Vaikuntha and merges with Him, and then brings the babies back to the Brahmana. This shows that Lord Krishna and Lord Vishnu are the same.
Another incident also comes: when, for the 18th time, Krishna defeated Jarasandha, He went to Gomantaka Parvata. There, Garuda came and crowned Krishna. Actually, in Vaikuntha, the devatas had gathered. Lord Vishnu asked all of them to close their eyes. Then Bali comes there and steals Lord Vishnu’s crown and runs away. Garuda chases Bali, defeats him, takes the crown from him, and reaches the Gomantaka Parvata, where Krishna was there. Garuda crowns that crown on Krishna’s head, thus proving Narayana Himself is Krishna.
Even when Lord Narayana comes on the earth as Srinivasa, and Lakshmi comes as Padmavati, in the first meeting of Srinivasa and Padmavati, Padmavati asks Srinivasa to introduce Himself. Srinivasa says, “My name is Krishna. I am from Chandravamsha. My mother is Devaki, and my father is Vasudeva. Subhadra is my sister. Arjuna is my friend. Pandavas are my cousins.” Thus, this also proves that Krishna and Narayana/Srinivasa are the same. Plus, Lord Vishnu, in the Bhavishyottara Purana Srinivasa Kalyana, shows a lot of dramas like not marrying Padmavati without Lakshmi coming from Kolhapura, etc. Therefore, He is paripoorna in every mood.
Now coming to which one do I like more personally, and why? I like Lord Vishnu and Krishna both. Actually, I should not say this, because both are the same. So, even if I say I like Lord Vishnu, it means I like Lord Krishna automatically, and even if I say I like Lord Krishna, then it would mean I like Lord Vishnu too. It is basically like saying, ‘There is a man named X who wears red goggles. He wore green goggles today. Whom do you like? The red-goggled person or the green-goggled person?’ Does that even make sense? No.
So, for me and the shaastras, both are the same and have no difference. I call Lord Vishnu by the name of Lord Krishna, and Lord Krishna by the name of Lord Vishnu. Today, I went to the Dhuma Lakshmi Narasimha temple, which is our Kuladevata. We had given a pooja seva, so we got the opportunity to do pooja to Lord Narasimha. I did the archana of tulasi to Lord Narasimha, chanting the Krishna Ashtottara Shatanamavali, and read Arjuna Kruta Durga stotra for Lakshmidevi. I kept calling Narasimha as ‘Krishna '! Krishna!’ like this. So, I don’t see any difference between any avatar of Lord Vishnu.
Even for Lakshmidevi, be it any avatara, be it Sitadevi, Rukmini Devi, Satyabhama Devi, Sridevi, Bhudevi, Durgadevi, Tulasi, Jayanti, Harani, Jayaa, Maya, Kruti, Shanti, etc., all are the same Mahalakshmi Devi only. There is no difference between the Moola Roopa and Avataara roopas of Lakshminarayana. Be it SitaRama, be it Rukmini Satyabhama Sameta Krishna, or Gopika Krishna (Gopikas having the presence of Lakshmi within them), LakshmiNarasimha, they all are the same Lakshminarayana, and not different from Him.
In simplest terms, you have Lord Vishnu. If the four arms become two arms and the same Vishnu wears a peacock feather and holds a flute, He is Krishna, and if He removes that peacock feather and flute and holds a bow and arrow, He is Rama. Coming to why I consider that? Because, first of all, the shaastras say so, the acharyas say so, and personally, I also feel the same, and it makes a lot of sense.
Hope this helps!
Jay SriRam!
SriAnantaroopadhara SriLakshmiNarayana Abhinna ShriKrishnarpanamastu!