While I am by no means a professional historian and I will defer to anyone who can provide a more in-depth answer, it's important to recognize the difference in geopolitical entities we're discussing here. More famous failed invasions of Russia, most notably Napoleon's and Hitler's, were being fought against not just Russia, but against a united Russia. As in, Napoleon and Hitler were facing off against a centralized, organized state with a single command chain, a single mind, a single will, a single army, etc. They were dealing with a wily foe that had access to great reserves of manpower and resources due to the organization of the state apparatus. The Mongols were not. They were dealing with a collection of small principalities with their own different laws, government types, ambitions, quantities of resources, even a completely different state structure; essentially, Napoleon and Hitler invaded a consolidated nation-state, the Mongols did not.

I do have some knowledge about Mongolian History, but not so much about russian history. I will try to answer as short and accurate as possible.

First off, as Comrade-Chernov mentions, Russia wasn't Russia back then. The main power-centre was a loose federation of east slavic tribes called Kievan Rus. The Mongol's invaded it partially in 1223, and fucked it over in 1236-1240 (which marks the end of Kievan Rus, and the beginning of Moscow as the regions power centre).

To compare the Mongol invasion to Napoleon or Hitler's, we gotta look at the logistics. One of the Mongols Army main advantages was their superior logistics. It's somewhat hard to compare to anything, let alone the French Army of Napoleon or the German Army of WW2. As you probably know, the Mongolian army (at this point atleast) was comprised of mainly mounted archers. Each soldier had 3-4 horses, and was able to pretty much live off the land. That gave the mongolians a huge advantage in mobility, and they were not affected by logistical problems. As long as the Mongolian horses had grass to eat, they could stay there a long time.

Another thing to take into consideration is the climate. Russia can be a pretty unforgiving place in the winter, but you know what? The Gobi desert (or anywhere in Mongolia really) isn't exactly a place to go picnicking itself. Both the mongolians and their horses are/were extremely hardy and weathered people.

Comrade Chernov mentions that the mongols did not face a united Russia, while this is for the most part true, it does in no way diminish the incredible feat of the Mongolian Horde. The Grande Armèe numbered over 500.000 when they tried to invade Russia. The mongolians used only 2-3 Tumens plus auxiliaries (roughly 50-60.000 of the forces. The sources are a bit shady here, and I can't confirm it 100%).

If you want to read more about mongolian history and their conquests, I suggest reading the Secret History of the Mongols. It's easy to find on PDF.