While not always true, your average game set in more civilised times tends to reach a grittier and more tragic point than the average fantasy game. While some Game Masters are skilful enough to make the wildest fantasy game feel realistic and gritty enough that every death matters or the most sedate and civilised countries feel playful and unserious enough that death is glossed over, generally it's easier to feel conflicted about killing in a modern world than a fantasy one.
And yes, naturally it does vary by player ... some players really couldn't give a damn about a fictional character no matter how lovingly evoked while others will find some way to empathise with a mass murdering serial killing undead squirrel enough to feel grief at their loss.
But generally, more often than not, it is easier to kill dozens of folks in a fantasy game without it feeling like murder while killing even a baddie in a Sin City-style modern world has a little kick of "Couldn't there have been another way?!"
I think it's partly because modern games tend to have a more linked in flavour than fantasy worlds. We're so used to orphan heroes and stand alone villains that we don't think in terms of the highly kincentric big family world that actually filled the medieval era. If you kill the evil king, there's no sense of loss to anyone. He was just this one thing - this particular archetype - and no one would mourn that.
Plus, and more importantly even than that, the NPC reactions help build that perception. If you clear out a thieves den in Fantasyland, the mayor will give you a medal and the locals will shower you in gold. If you clear out a thieves den in the modern world, well, kicking down the door to a slum and slaughtering the desperate denizens for pinching stereos and television sets just has a different sort of feel to it. If you were showered in gold for the act, you'd feel like you were in Sin City again and the average player would start eyeing off the Mayor as a better target for vigilante justice.
So I think it's also the context that surrounds the actions.
Thirdly, modern eras tend to sometimes, but not always, provide the sense that there might be an alternate option or at least there should be. Though certainly not standard in every modern-ish genre, generally there's a sense that in any post-Victorian game there should be another way even if there isn't. The greater the sense that jail is a suitable option, the greater you feel like a bad guy for killing folks instead. If you want television shows involving vigilantes, especially in the modern era, there's often a sense of loss of innocence and anger that there isn't a better way to go about things. The good guys feel forced to do bad things ... rather than happy to do what needs to be done.
Finally, and probably most importantly, modern games often colour their bad guys in shades of grey. This isn't always the case, especially with mooks, but those games that do give a sense of potential redemption in their bad guys creates more ambiguity by necessity. In many fantasy games, some races are bad by birth which creates a disturbing eugenics context when you look too deeply into it that allows many a forum rant about how a paladin doing their job right would slaughter infants in their cribs. Even in those races that aren't always evil, there's more of a sense that people can fall from grace then lift into redemption (also often a theme in modern games that have a lot of violence).
Now this last example certainly isn't true of all modern games. In a Call of Cthulhu game, the cultists are irrevocably evil so you don't feel bad about killing them. In a World of Darkness game, on the other hand, most creatures have some semblance of redemptive possibility in them (no matter how small) reflected in their final few morality traits left to them. Hence why the World of Darkness is so dark, you can't just slaughter people with moral impunity. You know you're doing the wrong thing for the right reasons.
But yeah, these are all my own meanderings so feel free to query, refute or outright reject my considerations in the comments below.