Kansas had a half decade of violence, on and off. Initially a lot of the issues between the two territories were just as similar as their organic acts, which are just copy and paste jobs in the same legislation with the territorial names swapped. A large number of white men of dubious residence, or quite clearly resident in adjacent states, came over the line and voted, held office, and so forth. That the Missourians did all this in Kansas produced a reaction, which had its own reaction and you end up with militias going around fighting small-scale battles, invasions of a thousand plus people aimed at destroying towns, arms shipments, vigilante violence, and so forth.

Just across the line in Nebraska the Missourians do come, as in Kansas, but they're met by antislavery Iowans who do the same. The situation quickly develops in Kansas that the proslavery party, hailing from Missouri, has an absolute lock on both the territorial government and election rigging. There is no solution for antislavery Kansans within the orderly political system, from which they progressively withdrew to create their own alternatives...which had the benefit of support from the vast majority of actual Kansans. In Nebraska, neither side is able to decisively rig things to their liking but they were able to get enough -or at least offset enough of the other side's cheating- to see the system itself as less than ideal but still viable. Thus there's no plausible excuse for the proslavery side to argue that the antislavery party are in rebellion and must be crushed by the sole legitimate government of the territory (TM).

One also has to consider that Kansas is occupied by white colonists, from within its first roughly six months onward, who include a large contingent of New Englanders and Midwesterners who came to Kansas specifically to keep slavery out. These are slow enough to arrive that the Missourians almost surely did not need to steal the territorial government, but they do form a powerful opposition to the proslavery party that can't simply be rolled over. In a fair election, before the Missourians really upped the fraud and violence, the two parties might well have been competitive. Up in Nebraska there are few such people and most antislavery types are local Iowans who simply do not face a proslavery party aimed at them. Free Soil is adequately dominant that Nebraska politicians hailed their territory as proving the success of the very policy that made Kansas bleed: letting the locals decide if they'd have slavery or not.

The closest equivalent to Kansas' troubles in Nebraska is probably what Nebraskans at the time called sectional, by which they meant North and South...of the Platte River. The territory's acting governor -the first guy died- had the authority to site the capital and chose to do so at Omaha. He also granted the territory north of the Platte more representatives than its population suggested. In certainly unrelated news, Acting Governor Thomas Cumming had a bunch of friends who did a bunch of land speculation up that way. This happened to place two-thirds of the white population on the wrong side of the river from their government, but it was quite within Cumming's powers. The legislature could theoretically pass a law to relocate the capital somewhere else, as was done in Kansas because of similar shenanigans, but Cumming stocked the legislature with that North-of-Platte majority so good luck with that one.

This prompted outrage with rhetoric that consciously emulated that used by antislavery Kansans, to the point of declaring that Cumming's tyrannical imposition of a capital was a species of revolutionary border ruffianism that exceeded Bleeding Kansas. They could make the same pointed complaints about non-resident voting, at least, but the stakes were far less. Whether Nebraska had a capital on one or the other side of the Platte was not a question of the territory's ultimate fate. Its main violent expression was a fistfight in the legislature. The opposition also floated a plan to annex the South Platte section to Kansas, which would Totally For Sure also fix the Kansas question, but the Kansans did not bite.

All of this underlies the fact that very few whites had any expectation that Nebraska would become a slave state. The Missourians had in Kansas a territory immediately next door to them -literally next door to Missouri's most enslaving region- with the same climate, watered by the same river, and clearly suited to growing hemp. Nebraska is not that, a fact which was visible on either side of the Ohio River. Hence the antislavery party from further East focus on Kansas, where the question is in doubt. The splitting of the remnant of the Louisiana Purchase in the Kansas-Nebraska Act was not done with the idea that one state would come in free and one enslaved, but that was widely expected and the Missourians were willing to concede Nebraska as part of the deal. The whole business of bringing states in two-by-two was always more a norm drifted into over time than a fixed practice, but even in 1854-60 it was enough of a thing to go assumed. Thus free soil aims look to proslavery men more like an attempt to roll back slavery by taking what rightly, to their minds, belongs to the enslavers. Nebraska, by contrast, was never really theirs and not much of a loss.

All of which makes the territory rather more boring than Kansas, which I'm sure its white inhabitants preferred. When slavery comes up directly, as when the legislature passes an abolition bill, Nebraska's governor is able to veto it with some controversy but without utterly alienating a large chunk of the territory. He did so by arguing finer points of popular sovereignty doctrine that would be anathema to most Kansans: per his reading of the law, nothing could be done against slavery until statehood. South of the border, that would have functionally been a declaration of slavery forever. North of it, there are few enslaved people and no coherent and explicitly proslavery party with a monopoly on formally legitimate power, so whites may convince themselves that this will all work itself out.