I tend to think of Kratos more in the line of "Dark Heroes" in general.
When characters like "The Punisher" started to become popular again after the fall of the Comics Code Authority, the stories involving such characters were quite interesting and involve some good analysis of the heroic "code against killing", the reasons for it, and the pros and cons of it.
However, as time went on the "Dark Hero" simply became an excuse to have comic books with massive amounts of ultra-violence and death, without much in the way of justification. For every "Punnisher" or "Wolverine" there seemed to be 10 costumed psychopaths running around destroying everything they could simply because they could, and wearing the label "hero" for some totally unknown reason. Heck, we even had a few psychopathic villains re-defined into heroes with only the loosest justification.
I don't think Batman is a good analogy for Kratos. Batman's big thing is he is unchanging, and is that way for a reason (so generations can appreciate the character, if they change him too signifigantly he won't be Batman anymore, and unrelatable to anyone who decides to revisit the character after a decades absence).
Kratos is like a Dark Hero that started out being an interesting work of writing, but then due to his popularity was kept around longer than he should be, and the focus shifted entirely to the ultra-violence "since that's what the readers want". After a while, you can't even understand his motivations.
The big reason WHY this makes him differant from Batman is that Kratos was created for a clearly defined story arc... one that ended. Batman on the other hand was created with a motivation that was left entirely open ended as it's an obsession. Oh sure after 70 years Batman's motivation is pushing it, but then again you have to look at why people are still interested in the character, and why he did the multi-generational thing. Kratos on the other hand a scant handfull of years old and unlike Batman was not defined in an open ended enough fashion to be franchise material to begin with (where Batman was conceived for potentially limitless episodic writing, as long as comic publishers could be found).
The big problem I see with Kratos, and one of the reasons why I have never been a God Of War Fan (and while I've goofed off with them, have never paid to get any of them... even used), is that even when there was an understandable motivation the plot existed to justify a bunch of violence, rather than the ultra-violence being an extension of the plot. Back when Game Informer covered the development of the very first game, they were making pretenscious claims comparing this idea to works like "Preacher" (comic series by Garth Ennis, and something I recommend everyone read). The first thought I had was some of the comments in Preacher's forward about emulation and how he sort of hoped nobody would try and duplicate it because they would fail and probably wind up with "meaness, for meaness' sake".... which is EXACTLY what happened with Kratos and God Of War and has become incredibly transparent by this point.
Wordy, verbose, and rambling, but that's my opinion.
Oh, and consider for a second I love horror, ultra-violence, and sex in pretty much all media. The thing is that I feel to be good these things have to be part of a decent storyline. On the surface I might seem like the target audience for "God Of War" but it failed to hook me because even in the beginning it seemed to BARELY hold itself together, which got my attention because of the things it was being compared to.