Societies that gained the least:

West Africa - contact with Mongols was very brief, and mostly resulted in war.

Western Europe - contact with Mongols was very limited. The Mongols only reached as west as Hungary.

West Asia - the Mongols had a very negative impact on the Islamic societies of the area. For example, Baghdad, at the time one of the most important cities in the world, fell to the Mongols, and was almost completely destroyed.

Societies that gained the most:

South Asia - The Mongols invaded India and set up the Mughal Empire, which resulted in great cultural achievements in architecture, painting, literature, and so on.

East Asia - The Mongols also invaded China and established the Yuan Dynasty, which ruled for over 150 years. They also tried to invade Japan twice, but were unsuccessful.