This is exactly typical of Natsume Youjincho, so you can expect what you already know and love about the characters, flow, and storyline.
The first arc with the The Waking Rock is one of the lighter, fun (silly) sided versions where it showcases the yokai interactions with each other and the general craziness that Natsume gets involved with. When that happens, you know the Dog Circle will be involved! Of course there is always a little lesson, and per usual, although simple, it makes it's point.
The second arc, The Strange Visitor, is the more serious of the two. It is full of the beauty, known pain, and ultimately the wholesomeness that is the other half of Natsume Youjincho. This one centers around Natsume and Tanuma and to me, a joy to see more interpersonal relationship growth with them and their unique shared and individual situations. The story itself is wonderful and befitting this OVA. Only downside is wanting it to be longer! Even though Nyanko-Sensei takes a backseat, it doesn't diminish a thing, it really only makes it better in this case.
The Waking Stone is what drops my review. As far as episodes go, it's a bit more disjointed than normal and seems to have gotten less attention in the animation department. If you don't know the series well, almost none of it will make any real sense. Fans will be fine and get it, but I'd give it about a 6/10. If it were a normal episode in the series I might be more forgiving, but added to an OVA situation, they could have done better in choosing a companion arc with a less chaotic dialog and flow.
The Strange Visitor, on the other hand, is exactly what we want and love. It's a 10/10. The animation is clean and has extra layers of beauty to many of the scenes. The story is well done and sound. I'd love to divulge more, but watching it and getting the feel is what matters.
All that said, this is why I've rated 9/10. Whatever the shortcomings of The Waking Stone is overshadowed by the great job done for The Strange Visitor. Happy watching fellow fans of Natsume and I hope this review helps.
***Newcomers to the series should definitely watch several seasons prior to watching this, I'd even go so far as to suggest viewing all 6 so that The Strange Visitor hits home with the most effect.***