I think full mastery in suttas was being like Moggallana and Mahakassapa
Please be explicit as to what ‘the two paths’ are.
I mean the two Arahantship path
That’s not explicit, please explain by name so readers can understand clearly.
In the title you mentioned Ven. Sariputta and Ven Mogallana while in the OP you mentioned Ven Moggallana and Ven Mahakassapa. Which one do you mean?
If you mean the Buddhas two chief disciples, then this might be true. Every Buddha has two chief disciples. Ven Sariputta was known for his insight while Ven Mogallana was known for his concentration and psychic powers.
I’m sorry I just mentioned Mahakassapa extra. Was thinking about him because Buddha was saying he was like his true son etc
“Two Arahant paths” is not correct, they are differences in emphasis on path practice, all paths to arahantship containing tranquillity and insight in some proportional relationship.
Both disciples were motivated to seek awakening through realization of impermanence (insight) as the Buddha also was (Upatissa= Sariputta, Kolita= Mogallana):
"Now at Rajagaha there was an annual event called the Hilltop Festival. Seats were arranged for both youths and they sat together to witness the celebrations. When there was occasion for laughter, they laughed; when the spectacles were exciting, they became excited; and they paid their fees for the extra shows. In this manner they enjoyed the festival for a second day; but on the third day their understanding was awakened and they could no longer laugh or get excited, nor did they feel inclined to pay for extra shows as they had done on the first days. Each of them had the same thought: “What is there to look at here? Before these people have reached a hundred years they will all have come to death. What we ought to do is to seek for a teaching of deliverance.”
It was with such thoughts in mind that they took their seats at the festival. Then Kolita said to Upatissa: “How is this, my dear Upatissa? You are not as happy and joyous as you were on the other days. You seem now to be in a discontented mood, What is on your mind?”
“My dear Kolita, to look at these things here is of no benefit at all. it is utterly worthless! I ought to seek a teaching of deliverance for myself. That, my Kolita, is what I was thinking, seated here. But you, Kolita, seem to be discontented, too.”
And Kolita replied: “Just as you have said, I also feel.” When he knew that his friend had the same inclinations, Upatissa said: "That was a good thought of ours. But for those who seek a teaching of deliverance there is only one thing to do: to leave home and become ascetics. "—Nyanaponika
Ven. Mogallana’s awakening was based on mindfulness of the body:
"I have heard that on one occasion the Blessed One was staying near Sāvatthī at Jeta’s Grove, Anāthapiṇḍika’s monastery. And on that occasion Ven. Mahā Moggallāna was sitting not far from the Blessed One, his legs crossed, his body held erect, having mindfulness immersed in the body well-established within. The Blessed One saw Ven. Mahā Moggallāna sitting not far away, his legs crossed, his body held erect, having mindfulness immersed in the body well-established within.
Then, on realizing the significance of that, the Blessed One on that occasion exclaimed:
With mindfulness immersed in the body
with regard to the six contact-media —
unbinding for himself."—Ud 3.5