" I am mainly interested in the resultant changes on the structure of the human society... I'm more interested in the handling of the threat than how the threat could be eliminated."
Extremely interesting question, Michael - but you simply haven't given us enough information about the world you're building. The only answer here is a resounding "It depends". You are asking an ecological question, and it's difficult to extract hard-and-fast answers from a whole system, such as an ecology, which is so full of feedback loops that every answer depends on everything else. :-)
Changes in human society would be driven more by the particular nature of the world and the predators that inhabit it. By "the nature of the world" I mean what kind of resources are available, and what constraints the world itself imposes; and by "nature of the predators" I mean very basic questions about the predators as a species.
To illustrate, let's take a not very weird example and look at some of the implications.
SETTING: THE VAMPIRES OF DEINDUSTRIAL AMERICA
Without going into the backstory in any detail, let's posit that vampires, in a more or less traditional form, have always been with us, but that they remained hidden: a very small population of predators who were able to keep their depredations on the DL throughout most of modern history. Vampires, as Charlie Stross pointed out in his blog (NSFW - language), are an excellent example of an apex predator on humanity - although sufficiently different from the Comanche example adduced above to underscore the point.
Anyway, there came a plague, some kind of pandemic that not only killed an awful lot of people worldwide, but irretrievably disrupted the essential networks of manufacture, information, and trade essential to worldwide industrial civilization. That civilization crashed and has not been reconstituted in any way at time of story. OK?
So we have a much-shrunken human population living in the ruins of their grandparents' civilization. Not only do they face problems of food production (industrial agriculture and distribution is gone; new patterns of land use urgently need to be established), there will be contention for resources... and yes, there will be contemporary equivalents of the Comanches, Mongols, or Mad Max gangs; but I am specifically ignoring them because this is only an example and not an actual story setting.
Now here's where it gets interesting. The pandemic that wiped out most of humanity didn't affect the vampires. The vampire population hasn't been much diminished. However, now we are looking at an entire species (in ecological terms) that can no longer remain hidden: they have to change their mode of predation because their attacks could no longer be concealed in the vast masses of humanity. (Not unlike the Kriegsmarine in World war II switching from lone U-Boat deployments to wolfpack tactics in response to an increasingly well-defended, target-poor environment.)
Instead of stealthy attacks against isolated individuals, vampires now attack, at night of course, in overt gang assaults. Mostly they don't turn their victims - too many vamps in the world already - they just need the blood.
So. What kind of human society will develop?
First, we're looking at more or less independent food production - field agriculture, gardening, animal husbandry. The vampire threat makes nighttime fortresses imperative; old buildings would be some of the likeliest. So, the core community of human society would be a vampire-defensible stronghold with contiguous agriculture.
Next, the vampire threat imposes some hard limits on the size of such communities. If the community is too small, there won't be enough people to work the fields/gardens in the daytime, and keep watch at night. On the other hand, if communities become too large, you lose the ability to know everybody personally. Mutual scrutiny, to identify bite victims or Renfields, would be a necessary part of survival. My experience as a sailor suggests that the limit here is something like 60 people: with a crew bigger than that, you just don't know everybody. You may know their names, but you can't reliably detect false notes in their behavior.
These communities would depend on salvage and scavenging. Rediscovery of more context-appropriate fabrication skills (blacksmithing, joinery, ceramics etc) has, at time of story, not progressed too far. (The benefit of a plague scenario is that there's a lot of stuff left behind with a rapid die-off.) Accordingly, communities without ready access to salvage sites would depend on itinerant salvage/tinker people - individuals or groups - for access to the leftover resources of industrialism.
That's the basic socioeconomic framework. Given that, let's introduce an actual example of the variability contingent on small changes in the specifics of the world.
EXAMPLE: WHAT DO VAMPIRES DO IN DAYTIME?
There's a general consensus (excepting the dumb as hell Twilight series, I guess) that vampires are very limited in daytime. In Dracula (the book) the Count is unable to move to defend himself when Jonathan Stoker opens the casket and hits the him with a shovel. In many other traditions, sunlight is actually destructive to the vampire: vamps burn up, or are at least badly scalded, when the sun hits them. What are the implications of choosing one or the other?
This simple difference would have a very significant effect on the human society, because it directly affects the offensive/defensive strategy of the humans.
CASE #1: Comatose by day
If the vampires are unable to awaken or move by day, they are incredibly vulnerable. A small, skilled, capable band of humans could wreak havoc in a nest of vampires: if you can kill any guardian Renfields (or human mercenaries), you can simply go from coffin to coffin, staking, beheading, or burning as necessary. In other words, humans would have an effective offensive strategy.
As for the vampires, their responsive strategy would be to disperse as much as possible, or else to establish such powerfully defended nests that the human teams would be foiled.
CASE # 2: Active by day, just staying out of the sunlight
This makes for an entirely different situation. A nest of awakened vampires, underground or otherwise out of the sunlight, would be far too formidable. Humans would not find it practical to assemble teams of hunter/killers, and would need to concentrate on defense.
Consequences for human society
These consequences would be remarkable.
In case #2, the communities described above would be unable to offer mutual defense. If vampires are attacking your stronghold some night, you can't expect your neighbors to ride to the rescue, unless they have remarkably powerful anti-vampire combat capabilities that would keep them reasonably safe during the ride. The implication: defensive communities would be much more isolated and independent.
By contrast, in Case #1, there would be a strong incentive for communities to collaborate to provide economic support for special-forces-type hunter/killer teams. As with the armored knights of medieval times, you need a large base to feed and equip a healthy individual whose only task is specialized fighting. Remember, the agricultural efficiency of the community is much reduced by the need for night watch and general defensive work. Removing a strong, healthy individual from the labor pool to perform specialist work is going to be a notable burden on a community of, say, 50 people.
So, let's develop that a bit.
In case #2, human societies would be small, communal, vulnerable to cultural and genetic drift.
We could probably extrapolate a high level of egalitarianism: When the vamps manage to break in in the middle of the night, everybody's staking. You don't care whether the person who destroys a vamp is male, female, old, young, a brawny blacksmith or a cook's helper. (Again, some personal experience here: when there's a fire on a boat or small ship, nobody hangs back. Everybody's got a job to do.)
Contacts between the communities and the outside world would presumably be largely confined to the aforementioned tinkers / salvagers.
This would tend to create a fragile, tenuous system, in which any kind of technological advances would be rare and slowly disseminated.
In case #1, by contrast, an economic and political arrangement like manorialism & feudalism would probably develop, simply for the purpose of being able to establish, feed, and direct those small, highly mobile teams of vampire killers.
Politically, this would probably lead to much tighter relations between groups of communities. It would tend to develop the fractal structure of the feudal model, in order to aggregate surplus to the necessary level of organization.
Socially, the feudal model tends to create much stronger class stratification, more distinct gender roles, and everything that goes with that. There would also be a much more favorable environment for scholarship, technological advances, and a more fertile matrix of social exchange.
So: there's the example, Michael. May you, and any other readers, forgive the length of it. Also, I hope you don't loathe vampire stories, or find the prospect of a deindustrial future unendurable. It's only an example. ;-)
Starting with a simple mash-up of postapocalyptic SF and traditional vampire fiction, I think I managed to demonstrate that a small detail of the predator species's characteristics - in this case, do vampires become forcibly unconscious during daytime? - can have remarkable effects on the answer to your question. In order to get there, though, I had to answer certain basic questions about agriculture and the development of a salvage economy.
If this example serves to illuminate the kind of interacting feedback characteristics that this sort of worldbuilding question demands, then it was well worth writing.