Counting on exact numbers, the eight banners yield 60,000 Manchu regulars. Possibly, there's a similar number of reservists, men too young or too old to fight. However, for campaigns out of their homeland, the Manchus rarely commit a large percentage of their main forces. When Nurhaci was fighting for his newborn state's survival in 1619, and when Huang Taiji fought the crucial Battle of Songshan, on each occasion the Manchu had at most 60,000 troops. Because of the numerical weakness of the Manchu state, therefore the Manchus relied heavily on Han and Mongol troops. Shang Kexi, Kong Youde, Geng Jimao, and other Liaodong militants probably offer the Manchus around 20,000 Han troops. Some of them are cavalry and infantry armed with matchlocks, but the most important gift to the Manchus were Han artillerymen. From the subjugated Mongols, the Manchus probably can call on 20,000 to 30,000 horsemen. So in 1644, the Manchurian kingdom can probably call on a total force of nearly 180,000 soldiers, and using the 1/3 rule (only 1/3 of the forces are readily available, the other 2/3 in training or off-duty), Dorgon probably led a force of 60,000 Manchu, Han, and Mongol combined arms force.

It must be remember that even though the Manchus were tough horse-mounted soldiers, they differ from the Mongol hordes, who are truly nomadic people. Unlike the Mongols, who relied on a herd-raising economy, the Manchus, like their Nuzhen ancestors, were much more sedentary. True, the Manchus are herd-raisers, but they are also part-time fishers, subsistence farmers, and miners. Even before Nurhaci's time, Manchus live in semi-fortified villages and hamlets, where they can trade farm goods, ginseng, and precious metals with themselves and outsiders. Perhaps, this is a reason why many would argue that the Mongols were hardier horsemen than the Manchus. It was no exaggeration that while the Manchus relied on the Han Chinese for manpower and firepower, they also relied on the Mongols for hard-hitting mobility.

I'm going to post it here too, which do you think would have won with both having around 100,000 troop at their prime. They both beten larger armies that have far superior numbers, I would go with Nurhaci because his enemies seem to be tougher and the odds he fought is also greater. Plus, his army is more developed in tech and organization than those of the Mongols of the 13th century.

Considering the two to be 3-4 centuries apart, of course they will be technological advances. If Nurhaci and Genghis both had the same tech levels and such, then it would be worth discussing. But since this is different techs at different time periods, there is no point in this discussion. Its like comparing a tank to a musketman of the American Revolutionary Army. Who will win? The tank of course.

"I'd off the bat go with Genghis Khan, but I don't know much about Nurhaci.
Could you say how Nurhaci's enemies were tougher and his odds harder? "

His enemy outnumberd him by over 3 to 1 and they are armed with firearms which the Jin army did not have when facing the Mongols. He was able to achieve this threw mobility and attacking each division of the Ming force before they join.
Nurhachi once defeated a tribal army that was 800 in size with only 4 men. He was only defeated by Ming because of Yuan Chong Huan's cannon which was not around during Jin. The Ming empire was much more powerful than the Jin at this time and even have Mongol allies which Nurhachi defeated in skirmishes.

Actually, both Genghis Khan and Nurhachi had united the tribes. This one's hard to say.