The issue is one of theme and presentation, not of content. There are plenty of games that have you mowing down civilians with machine guns. There are plenty of games where it's perfectly acceptable to be a total sociopath. There are plenty of games where the characters are unpleasant to be around, or at least they would be if you were around them in real life. The issue is that it ends up being unpleasant for the player, not just the characters, which games like GTA try to avoid. The difference between K&L and GTA is that GTA focuses on a sort of protagonist-centric morality, where only main characters are important and everyone else dies without much fuss, while K&L shows its characters as being as horrible as they would be in real life.
The two primary characters in K&L are, naturally, the titular pair. Kane is a former mercenary whose past has caught up to him. In the first game, he's told to retrieve a stash of money that he hid from his former partners - if he doesn't, his ex-wife and daughter die. Kane's daughter is his main motivation, and he doesn't really care who he has to be unpleasant to if it helps her. He's a classic example of moral myopia: he's an unpleasant person who does unpleasant things to people, but he's got his one focus that he tries to keep happy. He's undoubtedly evil, but he has an important attachment - in this case, an attachment that actually hates him because of his moral failings and irresponsibility.
Lynch, in the first game, is Kane's warden - there to make sure that he doesn't run off when he's told to go find his stash. He tends to simultaneously be the voice of reason (or, at least, disbelief) and the unreliable element that makes everything go to hell when he loses his medication. What's believable about his character, to me, is that he's not totally defined by being insane. He's got other motivations and can form attachments (as in K&L2), it's just that he's willing to do evil things most of the time and occasionally has lapses of psychopathic behavior. Notably, he's also an uncharismatic psychopath - he's not some badass sociopath, he's a creepy guy who kills people in gross and unpleasant ways.
The thing that sets them apart from, say, Niko Bellic or any other GTA protagonist is that Kane and Lynch theoretically exist in a "real" world. When they gun down civilians, it's meant to be as tragic as if they'd done it in real life. In GTA, the world is a sandbox full of jerks. Every sound clip is meant to reinforce how stupid the average civilian is, so it's okay to run them over with your car and it's no big deal. Friendly criminals can have wacky personalities and it's meant to be fun to watch. If someone the character likes dies, it's meant to be tragic, because you - the player - were attached to the character.
Kane and Lynch doesn't have that; crimes are depicted as being as cruel as they would be in real life, with little to no "gloss" or "glamor" to cover it up. It's all the same things that get done in other games, but it's presented in a way that shows that the characters in-universe disapprove as well. In most crime-related games, it seems like the running concept is that crime is totally awesome and fun and should be enjoyable. So what if the average person doesn't like it? Haters gonna hate. K&L, on the other hand, takes a more objective light, and by that light the player is allowed to see that these actions are actually pretty reprehensible, and even other criminals don't really like Kane or Lynch because of it. It's the same stuff, but presented in a way that doesn't hide the nature of their deeds.
Story & Narrative
K&L's narrative is largely defined by "things going wrong". In K&L1, the simple objective of "retrieve the money Kane stashed" is complicated by a bevy of other issues that arise. In K&L2, the game starts with something going wrong and then things never actually stop going wrong. This can be a bit of a "Diabolus Ex Machina" - i.e., things being bad for the sake of being bad. It stretches out the game's content, sure, but it feels fake to the player. It's certainly a change from the protagonists effortlessly accomplishing things without trouble and automatically getting a happy ending, but it's ultimately just as contrived.
This was especially prevalent in K&L2: almost the entire city is after you, and even though you mow down over a thousand people by the end of the game, nobody's ever like "yeah I think we should just let them go". It's one objective from near-beginning to end: Get out of Shanghai. The forces against you escalate so much that it's almost laughable, and lacks any sense of plausibility ("Wait, you mean they're sending soldiers against me now? Like, for real?")
Kane and Lynch's main problem is that there's not a lot of logical buildup to things going wrong. After all, "things going wrong" is a pretty solid plot motive, but in this case it's not supported. It just turns into guaranteed failure after guaranteed failure, with no real hope of redemption or success. It's fine to subvert the audience's expectations about the character's automatic success, but that requires that they think that "automatic success" will occur. As it is, K&L's narrative is just as predictable, but from the other direction.
Kane and Lynch is a gritty game. It knows it's a gritty game. It desperately wants to be a gritty game. The entire style of K&L2, for example, was patterned after camcorder footage ripped straight from COPS or some similar show. The desire for "grit" becomes even more obvious when you factor in the trailers, which attempt to depict gore and violence as "realistically" as possible. Everything about the game, from level design to character modeling, is meant to evoke a very realistic sensibility similar to a live-action gritty crime film. If you just played the game without shooting, it would seem pretty damn immersive, especially when it comes to stuff like the nightclub level in Dead Men.
For me, though, this fell apart as soon as gameplay actually started. As I've discussed before, it's hard to create a game that establishes concepts like "realism" and actually follow through with it. In this case, the game is so gritty that I was actually surprised in K&L2 when the game actually started being a game. The game up to that point had felt so immersive and realistic that as soon as all the usual game stuff showed up (ragdolls, regenerating health, bullets that don't damage clothing or flesh but just explode in globs of red jelly) it felt ridiculous and disconnected from the narrative.
It's even worse because the trailers focus on a very grounded sort of gunplay, where the sounds and impacts are emphasized and a bullet wounds someone fairly realistically. If you watched the trailers, that's the kind of stuff the game would seem to be about. If you played the game, on the other hand, it's a genre-standard Gears of War cover shooter - and it has to be, because it's first and foremost a third-person shooter. It's like that for the same reason every other game is: because if you make a game about shooting, there's not enough you can do to avoid getting shot while still actually having a lot of content.
These issues can be divided into necessary and unnecessary. For example, the horrible guns in both games were unnecessary: giant globby yellow tracers that moved too slowly mixed with inaccurate, poorly-handling guns just made the whole thing feel extremely fake. It's hard to buy into the idea that guns are realistically deadly when it takes a full magazine to down someone a few yards away from you. It's the kind of little thing that takes away from the game's overall presentation: here we are led to believe that this is like reality, and then the necessities of gameplay and stylistic decisions start to aggressively intrude on the concept.
To me, Kane and Lynch is a good movie attached to a bad game. All of the bad parts come from gameplay, including the narrative "things go wrong" problems, which are necessary to stretch out the gameplay from a very thin premise. In every respect except the gameplay, it's excellent - presentation, design, characterization, and so on. It presents a grim and gritty look at criminal heists in the same way that movies like "Heat" do, and for once it seems like criminal protagonists are being treated like psychopaths instead of jokingly tolerated. It's the necessities of gameplay that drag it down, because as much as it would be nice, games aren't "real" yet. People who get shot look fake, the bullets look fake, the guns feel fake. Everything that has to do with gameplay feels totally unreal and it just drags down the rest of the game with it.
So, To Sum Up
1) Kane and Lynch is a good movie because it presents an unflinching look at traditional notions of the "heroic sociopath" and can actually make jaded gamers feel awkward about blood and gore and murdering civilians simply because of how it presents them.
2) Everything about the actual "game" parts of K&L undermine this by feeling fake and unimmersive.
3) Some of those things are necessary technical limitations (ragdolls), some are necessary gameplay choices (regenerating health), and some are just kind of a pain (the way guns handle).