Comparison to First Season
In my opinion, the first season of Noragami wasn't bad by any means, and actually got really good towards the last episodes, but lacked the excitement in the beginning. And I'm not just talking about how anime normally starts slow. Here, it was so slow that I can see why some would become uninterested in it pretty quickly. But if you got through the first season, this time it's nothing like before. The action picks back up right away, and most of the time things never get too dull.
Season 2 Synopsis
Aided by the character development from season 1, the second season continues to show how important relationships are between gods and Regalias, and how one's (or a group's) hidden pain will only end up hurting them. This perspective allows the viewers to understand the bond and communication that these two sides require, and it's quite an enjoyable experience to see.
Positives
This season involves Hiyori a little more, giving her a little more of a significant role instead of just being around during the action (obviously excluding the times where she kicks the hell out of some Ayakashi), being able to save both Yato and Yukine a few times. This development fully gives the trio a sense of unity, like they're a true team now, when before it seemed like Hiyori was only around just because Yato promised to return her body back to the way it was. Yukine also receives more character development, even though he received plenty in the first season (not to say that character development isn't welcome). Lastly, the most prevalent gods in the anime all receive a lot of attention, especially when looking into their past. It solves a few questions you may have had about Yato in the first season, and gives more insight into why he has certain relationships with certain characters. It's very interesting to see how everyone's history intertwines in a way that resulted in the current situation.
Negatives
Perhaps the biggest negative of this entire show is that it often goes from action-packed moments that leave you excited and ready for more to several long minutes of dullness, greatly diminishing the excitement that you may have just felt from what just happened before. This throws off the flow of the entire show, leaving you with what I can only describe as a roller coaster of emotions throughout the entire thing, and not the good kind.
Conslusion
I'm giving the second season a 95 because it manages to grasp the attention of the viewer the whole time, continues to build character relationships in an interesting way, and ends on a note that truly makes you want to see more (Also, the OP is an absolute banger). The only downside I can point out is the aforementioned roller coaster ride of emotions that detract from the experience a little. Understandably, there's a purpose to these dull moments, but they still detract from your experience because of the exciting moment that happened only a few minutes prior. Other than that, it's an excellent anime, and I definitely recommend watching it, especially if you've already seen the first season.