I'm currently reading through Jonathon D. Spence's The Search for Modern China. In chapter 4, under the section entitled "The Center and Channels of Power," Spence discusses how Yongzheng was able to use newly consolidated power to better coordinate his forces against both the Zunghars and the Miao. Why were the Miao subdued while the Zunghars were able to achieve victory against the Chinese forces and were only defeated during Qianlong? Any clarification and additional details on these events would be much appreciated.
You can't really compare to the Miao to the Zunghars. The Miao were composed of tribes and probably numbered only into the thousands, whereas the Zunghars had a centralized state and a much larger and better army.
The reason for the Qing loss in 1731 was primarily due to Yongzheng's aggressive ambition. Peter Perdue explains that this was an "imperial overstretch," as the rough terrain made it difficult to the Qing army to supply and the Qing, despite having a much larger army, was less mobile and was subject to constant raids and harassment. The Qing general Furdan made a very stupid mistake in pursuing small enemy raiding parties, until they ultimately lured him into an ambush, where the Zunghars trapped him with an army twice his number. Of the 10,000 men he sent out, only two thousand returned alive. With Furdan defeated, the other army under Yue Zhongqi was forced to withdraw.
As Peter Perdue explains:
Yongzheng's aggressive ambitions had led to a military disaster, the first major defeat of a Qing army by the Zunghars. Driven by the goal of surpassing his father's glories, Yongzheng violated his own instincts for cautious retrenchment. Once again, tried-and-true nomadic tactics had lured an army from China beyond its supply lines and destroyed it. Retrenchment and stabilization of the border became the main watchwords of Qing policy for the next twenty years.
See: Purdue's China Marches West: The Qing Conquest of Central Eurasia