I remember reading the Punisher comic books when they first came out. One of my friends had the entire first year and, considering our quasi-military fandom at the time, we read them with intense interest. This series modernizes the character in many ways to make him and his story much more believable, but is still true to its original roots.
Part of the strength of this superhero series is that it's not really a superhero series, just as the Punisher isn't really a superhero. Instead, this show addresses head on some difficult topics of today's world, especially in the areas of how we treat our veterans and the questions about the 2nd Amendment. It does not provide easy answers, but rather opens up the debate in a (mostly) realistic and honest manner.
My favorite part of the show is how true the characters are to their motivations and situations. With only one or two exceptions, the characters behave as though they were real people rather than Hollywood caricatures. Even when characters were not doing what I would want, they were believable in their choices.
This is not a family-friendly show. There were some parts where I felt it might even top, or at least compete with the violence of Game of Thrones. However, it tells a story worth telling, and it does so in interesting ways.