Sadl al-yadayn - leaving the hands open by the side during prayer - is for sure the more authentic practice and was clearly the practice of the Prophet Muhammad (s) and the people of Madina. It was also the practice of Imam ‘Ali (a) and those who followed him, his Shi’a, and also the later Imams such as Ja’far al-Sadiq (a). It was even the practice of the Khawarij who seceded from the side of ‘Ali!
Basically sadl al-yadayn was the only practice for the Islamic prayer until Mu’awiya commanded people to pray with qabd (folding the hands).
I haven’t read a reason for it but my own understanding is that he may have wanted to test the level of religious control he had over his subjects. Abu Hurayra is said to have been in the camp of Mu’awiya during the civil war but he sometimes used to pray behind ‘Ali. It also created a very immediate and visual indicator of which political side a praying man belonged.
As happened with many other matters of this nature in that time period of the Fitna, the hadith fabricators created fake hadith to retrospectively create support from the Prophet (s) for qabd al-yadayn.
As such, the Sunni schools of fiqh accepted both positions of sadl and qabd. It is interesting to note that all four Sunni Imams of fiqh accept prayer as valid with sadl, and that remains the valid lowest common denominator. And of course, as we know, the Maliki school advocates sadl as the correct approach.