Try
Baccano!, it's set at the end of the 1920s and the beginning of the 1930s with 3 major storylines told the same way as in "Pulp Fiction". It is generally serious and realistic but there are also comical moments (everthing that involves the character duo Isaac and Miria) and immortals play a major role too, but that is really cool and shouldnt bother you.
Dont forget to watch the 3 DVD specials released by BSS, they continue the story as ep 14-16. I's also recommend to watch the series twice because you miss a lot of pretty cool details in the first episodes when you're not familiar with the characters and story.
other recommendations:
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Jin-Roh, a movie about a special force set in Japan after an alternate end of WW II.
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Texhnolyze, cyberpunk setting, gets really intense towards the end.
series involving guns but are not that realistic/serious:
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Grenadier
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Black Cat, Manga version is a lot better though
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Sunabouzu, post-apocalyptic setting
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Trigun