The two aren’t mutually exclusive, but while arquebuses may have played a part, the hand to hand fighting lasted for hours and was the decisive factor. From Wiki...
“Around noon, first contact was made between the squadrons of Barbarigo’s and Sirocco, close to the northern shore of the Gulf. Barbarigo had attempted to stay so close to the shore as to prevent Sirocco from surrounding him, but Sirocco, knowing the depth of the waters, managed to still insert galleys between Barbarigo’s line and the coast. In the ensuing mêlée, the ships came so close to each other as to form an almost continuous platform of hand-to-hand fighting in which both leaders were killed. The Christian galley slaves freed from the Turkish ships were supplied with arms and joined in the fighting, turning the battle in favour of the Christian side.
Meanwhile, the centers clashed with such force that Ali Pasha’s galley drove into the Real as far as the fourth rowing bench, and hand-to-hand fighting commenced around the two flagships, between the Spanish tercio infantry and the Turkish janissaries. When the Real was nearly taken, Colonna came alongside with the bow of his galley and mounted a counter-attack. With the help of Colonna, the Turks were pushed off the Real and the Turkish flagship was boarded and swept. The entire crew of Ali Pasha’s flagship was killed, including Ali Pasha himself. The banner of the Holy League was hoisted on the captured ship, breaking the morale of the Turkish galleys nearby. After two hours of fighting, the Turks were beaten left and center, although fighting continued for another two hours.[37] A flag taken at Lepanto by the Knights of Saint Stephen, said to be the standard of the Turkish commander, is still on display, in the Church of the seat of the Order in Pisa.”
Yes, you are right, there are many different perspectives of how the fight went down. The Catholics should have lost. There was a key wind change that made a huge difference in the outcome at the very beginning of the engagement. Jack Beeching’s rendering of the battle is riveting. Especially what Don John of Austria did with the Spanish galliard. It was so awesome, you will have to read it, don’t want to spoil it for you.