(1) The Comanche, Kiowa, etc. had solid herds of horses since they lived far enough south that severe cold didn't hurt their herds as much as in the Central Plains or Northern Plains. They were the conduit for more northern groups to get more horses either through trade or by force--let's recall that one of the key measures of a warrior in many of these societies was stealing the enemies's horses, since north of Kansas winters are more consistently cold and thus those groups required more replenishing of their herds. The bison thing is very true--one writer describes them as "a weed", since bison numbers were so huge because all their competitors (larger bison, horses, other megafauna) went extinct leaving the bison as dominant. Since no group could kill enough bison to put any real dent, they didn't have a real cultural concept of overhunting bison (of course they noticed when bison numbers were low like during droughts). Incidentally this drove their expansion since they so relied on bison for both themselves and external trade that during droughts they needed to push into the lands controlled by other people which prompted conflict. It was a self-perpetuating cycle--they needed more bison so they expanded to take the hunting grounds from another group which if they won would give them more bison and land for their horses which to maintain that new equilibrium pushed them into yet more conflict in the next time of need and so forth.Thanks, all. So major differences are (1) the Plains Indians lacked domestic herds and had not had sufficient time on horse back to come to some kind of stable, enduring relationship with bison--which meant their populations were less and (2) the Plains Indians mostly lacked the access to tribute and loot from settled civilizations around their periphery, which would have allowed for greater and more complex military and state development. Though the Comanche/Kiowa may have been a proto-example of this phenomenon, and maybe the exception that proves the rule
(2) Their version of tribute was enacting it from more sedentary peoples, and there is archaeological and early historical (i.e. 17th-18th century) records of this being the case. The settled farming villages in the river valleys of the Plains to some extent relied on more nomadic hunter-gatherers for bison hunting, and in turn, the bison hunters relied on them for additional food and other goods. The actions of the Comanche, Lakota, etc. were an exaggerated and extreme version of this tradition made possible by the reintroduction of the horse to the Plains, although not totally explained by it since even in the remote corners of the Plains (like in modern Montana with the Blackfoot, Shoshone, etc.) they were influenced by the European fur trade and indirectly by the Spanish whose trade ended up bringing horses and guns to that area before long.
I am not certain if this ecological issue was as much a factor on the Eurasian steppe, but it is certainly a major factor in explaining the actions of the Plains Indians. Considering their reliance on the bison and cultural reluctance toward shifting to other lifestyles (they had a taboo against eating horse meat for instance, and cattle herding was adopted very late--the Comanche did so in the 1860s), they were pretty much doomed to some manner of collapse (worse than before) making their dominance ephemeral. The United States simply was in an inherently good position to exploit this collapse and gained an even greater position thanks to the subsidised bison hunting.
It's also worth noting that among the Plains Indians there was no concept of a khan or other leader, since leaders gained their status solely by means of achievements (in hunting, combat, etc.), and their heirs only had status because they'd inherit their predecessor's wealth. While large gatherings of tribes existed, they didn't have the ability to coordinate campaigns or anything.
Some Plains Indians were on the Plains for quite a while, like the Kiowa who split from the Ancestral Puebloans, although the majority (i.e. Cheyenne, Lakota, Blackfoot) expanded there and adopted a new lifestyle as a result of no other option since they were evicted from the Eastern Woodlands as a result of conflict spurred on by the fur trade and the Indians who benefitted from it. It's interesting that the local peoples, like the Caddoans (who did a great job against the Comanche OTL, and it's a testimony to Comanche skill they managed to expand into Caddoan lands) or Mandan, failed to do so, although this is more because they had a successful lifestyle beforehand (farming in river valleys and trading for whatever they couldn't gather/hunt) so lacked the "desperation" of other groups--the Plains Indians thrived in some years but starved in others, and that drove their militancy. Also because they disproportionately suffered from disease thanks to their more sedentary lifestyle in addition to events like a US vaccination program of Indians which vaccinated many Lakota but ran out of money before other groups could be reached. The river valleys were also key trails west which meant they ecologically suffered (i.e. cutting down trees for firewood, oxen/horses overgrazing, etc.) before the rest of the Plains.The Plain Indians only spread into the plains about a century before settlers starting moving north and west into their territory. Those settlers were technologically advanced, backed by advanced and aggressive societies.
Have steppe tribes had to deal historically with technologically advanced neighbors that were themselves expansionist? The only thing I can think of is the Russians moving on the current Ukraine / Crimea area but I don't think those were classical steppe nomads.
As I noted, the factor of adaption to the "Plains Indian" lifestyle was often out of desperation, and arguably they often did fight from a position of weakness. The problem hit them big time when the enemy they were fighting wasn't another Indian group with similar technology or isolated outposts of an overextended empire but an empire hellbent on expansion and very capable of supporting it. They'd backed themselves into a corner where they choice was to submit to the United States (and everything negative that brought with it) or fight them and understandably many chose the latter.