Which is better: Night vigil (Qiyam al-Layl) or remaining in the mosque after Fajr until sunrise, especially in Ramadan, if it is not possible to combine them both?

The first and best option is to combine night vigil (Qiyam (definition) al-Layl) with staying in the mosque after Fajr until sunrise, for whoever is able to do so, while taking a period of rest at night to facilitate this. This is the guidance of the Prophet, peace and blessings be upon him.

If performing the entire night vigil conflicts with staying in the mosque until sunrise, then prioritizing the night vigil is more important, especially during the last ten nights of Ramadan (definition), because reciting the Quran at night is better, and because night prayer is more conducive to concentration of the heart, further from distractions, and more safeguarded from ostentation.