While both the comic and the film have pretty heavy usage of violence, here is what I think is the key difference. Alan Moore and Dave Gibbons knew what to emphasize and what to imply. For example, the scene with the devastation in New York after the squid attack with all the bodies lying around and the absolute silence it conveys is not just for shock value, but also communicates the horror of what Adrian has done, especially since some of those citizens had speaking roles and where characters in their own right. Likewise for the Black Freighter, in which the wrecked sea Captain has to make a raft from his dead shipmates. That's graphic violence used appropriately and in context.
Zack Synder, on the other hand, doesn't seem to grasp the fundamental concept of less is more. Whereas the graphic novel did show Doctor Manhattan exploding bodies, it was more or less quick and efficient. Here, Synder dwells upon the remnants of the gangsters in the club, including a shot of a mangled arm dangling from the ceiling which was never in the original comic. Likewise, he makes the fight Dan and Laurie have with the gang members MORE violent and actually has them kill a few of them, which is really out of character for both of them and makes them on the same level as Rorscarch. And of course, there's the embleishment of how Rorscach kills the child murderer with a cleaver repeatedly instead of burning the guy--a death which actually happens off panel, BTW, and is far more effective, suspenful, and chilling as a result. And while one can understand Synder's decision to have the thugs arms get sawed off in the prison scene rather than his throat silt, it still is needlessly excessive.
So, not only is the film version of Watchmen more violent than the source material in that respect, it is needlessly so.
