Simple answer is that both are destined for liberation at the same time.
Both Crocodile and Elephant are the ministers under a same king named Alakesha in their previous lives. Elephant was Parshvamauli and Crocodile was Ghanöanada. So, they both were colleagues.
Shri Narada said: The sages tell an ancient story of how by simply
seeing Cakra-tirtha one becomes free of all sins. There once was a
great, pious, and wealthy king named Alakesha, who performed a
Vishnu-yajna on the summit of Mount Kailasa. ..................... Karttikeya worshiped the assembly.
Kuvera's two ministers, Ghanöanada and Parshvamauli, who were very
generous and most learned in the scriptures, were also there. In this
way the yajna, carefully performed according to the rules and
regulations, was a great and festive success.
[16-23, Chapter 10: In the Description of the Gomati River, the Glories of Cakra-tirtha, Canto 6, Garga Samhita]
Sage durvasa cursed them out of anger. The reason was their greediness. The curse on Ghanöanada is to become Crocodile and the curse on Parshvamauli is to become an Elephant.
Shri Narada said: Hearing these words, generous and charitable Kuvera
said, “Yes. I agree. Please take them. As Kuvera was about to give
the nine treasures, his two ministers, Ghanöanada and Parshvamauli,
who were bewildered with greed, spoke. The two ministers said: What
will this greedy brahmana do with those great treasures? Give him a
hundred thousand other things and keep the nine great treasures for
yourself. Shri Narada said: When he heard these harsh words Durvasa
became filled with anger. His eyes were red and his eyebrows knitted
with anger. For the time of two eyeblinks the entire universe shook.
Seeing Kuvera humbly bowing down before him, Durvasa Muni proceeded
to curse the two ministers. Shri Durvasa said: Sinful, wicked, greedy
Ghanöanada, you clutch at wealth as crocodile would clutch. I curse
you: Become a crocodile! Sinful, wicked, greedy Parshvamauli, you are
pushy like an elephant. I curse you: Become an elephant!
[34-40, Chapter 10: In the Description of the Gomati River, the Glories of Cakra-tirtha, Canto 6, Garga Samhita]
Since both are devotees of Vishnu, they approached Vishnu after getting curse and Vishnu gave assurance to the both
Bewildered by the brahmana's curse, Kuvera's two unhappy ministers
took shelter of Lord Vishnu. The Supreme Personality of Godhead said:
You two worshiped Me in the yajna, but now you are unhappy. I have no
power to negate the words of the brahmanas. You will indeed become a
crocodile and an elephant. You will fight, and by My mercy you will
regain your original natures.
[1-3, Chapter 11: In the Creation of Cakra-tirtha, the Liberation of the Elephant and the Crocodile, Canto 6, Garga Samhita]
After becoming animals, they had severe fight with each other. Exhausted Elephant gets the knowledge of past lives and prays for Vishnu. Vishnu then liberates both.
Shri Narada said: After Lord Vishnu had spoken these words, Kuvera's
two ministers became a crocodile and an elephant. Nevertheless, in
their new station they could remember who they had been before. For
one hundred years Ghanöanada was a fearsome, feroicous, always angry
crocodile in the Gomati river. Parshvamauli became a regal elephant in
the forest by Mount Raivata. He was a hundred dhanus tall. ........ As
many saintly persons watched, the crocodile and the elephant fought
for fifty-five years. Finally the elephant, now exhausted, remembered
his previous birth. Finding himself almost caught in the noose of
death, the elephant remembered his previous birth and took shelter of
the feet of the Supreme Personality of Godhead. The regal elephant
said: O Shri Krishna, O friend of Arjuna, O dark Lord, I offer my
respectful obeisances to You. O master of the gods, O Vishnu, O
perfect Lord, O supreme purifier, O glorious one, O Supreme
Personality of Godhead, please, please save Me! Save me from the noose
of my past sins! Shri Narada said: Aware that the elephant caught in
the crocodile's grip was remembering Him, the Supreme Personality of
Godhead, who is kind to the distressed, picked up His sword and flew
to that place. Descending from Garuda, the Supreme Personality of
Godhead threw His cakra and wonderfully severed the crocodile's head.
As a person may suddenly lose all his wealth, that spirit soul was
suddenly pushed out of a crocodile's body. After killing the
crocodile, the Lord's cakra continued until in finally landed in a
lake, turning all the stones there into incarnations of the cakra. .... His head
severed, the crocodile attained his original form of a god. By the
mercy of Lord Krishna, the elephant also attained the form of a
god. After circumambulating the Lord, bowing down before Him, and
offering prayers fwith folded hands, Kuvera's two ministers returned to
their own abode.
[4-23, Chapter 11: In the Creation of Cakra-tirtha, the Liberation of the Elephant and the Crocodile, Canto 6, Garga Samhita]
Coming to the intention of the question, there is no explicit priority here. Both were devotees of Vishnu and both were destined to liberation and hence Vishnu gave liberation to both of them. The implicit reason for priority in cutting crocodiles head is obvious i.e., to save Elephant quickly. Else there is no priority. Since the elephant remembers the past lives and prays Vishnu, which was not happened in the case of crocodile, the prayer of elephant may became famous.