There is no such thing as staying up whole night in sunni-shia-sufi Islam.
"And it is Allah Who has ordained the night as a garment for you, and the sleep as a repose of death, and the day as the time of return to life." (Quran, 2547)
Night is a garment on human beigs for sleep and no Muslim denies this. But staying up at certain parts of the night for dhikr (remembrance of the Lord) and prayers is a suggested thing. There are suggested prayers at nights
"And from the night, pray with it as additional for you; it is expected that your Lord will resurrect you to a praised station." (Quran, 1779)
And such recommended-additional prayers form an important role in a Muslims' life especially in Ramadan and Qadr night.
And the shias said taravi was forbidden.
peace
As far as I know shia Muslims don't say it is forbidden. They have alike voluntary prayers with sunnis. But the difference is that sunnis usually pray it in congregation whereas shiites pray it individually. And in total most sunnis pray 600 rakah (cycles) at nights in Ramadan whereas shiites pray 1000 cycles.
So, shia Muslims don't say it is forbidden. What they say is praying it in congregation is an innovation. Because only the compulsory prayers can be prayed in congregation. Here's an article on the shia Islamic stance towards tarawih http//www.al-islam.org/nutshell/files/tarawih-tr.pdf