Well,Who knows what would happened if Qing was close to Europe.I believe manchus would did much better than what ottomans have done.They were so eager to learn new technology before they got drown in the peace and they were so powerful and fearless that they conquered the whole mongol hordes that no other chinese dynasty were able to do.
While it is true that Qing did conquer the Mongolians, it really didn't establish firm control over them. The Mongolians, similar to Tibetans, are vassal states of Qing Empire. This means while the sovereignty of these lands and the people belonged to Qing dynasty, it did not establish firm administrative control over these regions----administrative control was actually established by PRC.
Of course, arguing Qing is powerful because "no other Chinese dynasty were able to do" is a rather absurd standard. For one thing, the Mongol's history isn't long at all. In fact, their entire race only existed for a grand total of three Chinese dynasties, the Song dynasty, which by the time the Mongols actually formed a nation, was already very old. Ming dynasty, on the other hand, managed to shatter the Mongolian nations and broke it down into small tribes. In fact, the reason Qing was able to gain sovereign over the Mongolians tribes was because Ming managed to splinter the Mongolians to such an extent that they simply could not resist.
Also, there are certainly other Chinese dynasties that extend its influence over Mongolia region. For example, Han dynasty defeated and drove out the Huns (or Xiongnu). The Tang dynasty also have protectorate reaching the Gobi desert.
The problem with Qing from the very start is the fact it is a minority race establishing dynastic control over a much larger race. In order to maintain that control, they implemented policies which discourage education and expansion of ideas. For example, the content of education and bureaucratic selection is restricted to the Four Books by Confucius. In comparison, PRC's national examination include Math, Chinese, English Physics, Chemistry, Biology, Politic, English, History, Geography and Information Technology. The bureaucratic selection today would have include extensive examination of knowledge on the appropriate post. As a result, scientific progress during Qing dynasty stagnated.
I know that due to movies and online novels, some Chinese youths are obsessed with this idea of "nomadic warrior race" and think it is a romantic concept. It is not really that surprising considering in the west there are also lots of games based on "savage barbarian warriors beating civilized, but coward farming race" (warcraft anyone?) In practice, however, nothing can be farther away from the truth. For starters, nomadic society are NOT better at war than agricultural society by a long shot. Historically, nomadic societies are really only capable of defeating agricultural ones when the latter is having severe internal problems. For example, the rise of Mongols are due to internal conflict and corruption of the Jin empire, which itself was a nomadic society that rose due to corruption and internal conflict of the Liao empire. In comparison, Mongolian tribes come and goes by the thousands during earlier reign of the Liao-Jin period and they are not worth a footnote in the history.
The reason for this is because generally speaking, wars are fundamentally fought with resources---manpower, weapons and supplies. Tactics are important but it will only take you so far. As a rule, nomadic society generally has much smaller population than their farming neighbors for the simple fact nomadic society simply doesn't have enough production to support a large population.
Weapons and armors require a certain technological level and social infrastructure, which is firmly to the advantage of agricultural society. So forget about the barbarians wearing full plate armor wielding large steel axes. Plate armor is quite difficult to make. Most nomadic society also have problem producing even basic iron tools, let alone making steel ones. One of the reasons for Mongolian ferocity is that they managed to acquire technologies from Song dynasty, which was the largest steel producer in the world at the time and also quite advanced in gun power based weapons. In fact, the weapons that cracked walls of Song dynasty's cities were Arabic in origin.
In term of supplies, nomadic societies also tend to be at significant disadvantage. Supporting an army is a very expensive effort. While powerful agricultural societies may have supplies to fought a prolonged conflict, nomadic society often have to rely on pillaging the locals just to get past the first few month. In fact, most of the nomadic incursions will be stopped after a few days due to the nomadic running out of food. In order to successful to sustain the army through pillaging, the target has to have very weak border army, almost no second line of defense, can't reinforce the existing army and have crumbling city defenses. All these conditions can only happen when there are serious internal problems. For example, Mongolian rise is due to decline of Jin empire and Ottoman rise is due to decline of Byzantine empire.