Did British Empire and Mughal Empire exist in the same era?

Yes, the two civilizations both existed around 1583 CE.

Which lasted longer, British Empire or Mughal Empire?

British Empire lasted longer (414 years).

British Empire: Avrupa; Mughal Empire: Güney Asya

British Empire (1583 CE – 1997 CE) and Mughal Empire (1526 CE – 1857 CE) lived in the same era.

The empire with the most extensive territory in history. It was referred to as "the empire on which the sun never sets."

The greatest Muslim empire of India. The Taj Mahal was built during this period. It produced 25% of the world's GDP.

Did British Empire and Mughal Empire exist in the same era?: Yes, the two civilizations both existed around 1583 CE.
Which lasted longer, British Empire or Mughal Empire?: British Empire lasted longer (414 years).
Which regions did British Empire and Mughal Empire rule?: British Empire: Avrupa; Mughal Empire: Güney Asya