Why I like the first season of Mushishi much more than the second
When I look back at the first season of Mushishi, what really sticks in my memory is not the individual stories but the things we learn about the mushi, the mushishi, several recurring characters, and especially Ginko himself. In particular, learning more about Ginko over the course of the first season added special poignancy to any number of moments; for example, when Ginko turns down an attractive offer to stay longer with a family rather than venture out into the snowy winter, we already know that he can't accept because too many mushi will accumulate around him if he stays in one place. One of the joys of the first series for me is the slow illumination of who Ginko is and how the series quietly explores his character over the course of the show.
The second series is almost entirely lacking in this and many of its efforts in this direction seem half-hearted. I don't think this is the fault of the series itself as such, because the honest truth is that the first series already covered a great deal of ground as far as the mushi, the mushishi, and Ginko himself go. This leaves the second series with not that much extra it can say. But the unfortunate result is that the second series has wound up being far less about Ginko than the first series was and there are only a few moments that are amplified by what we know about Ginko.
For me, this creates a series that feels nice but not essential in the way the first series was. By the time it finished, the first series had pretty much given me all the answers I feel I needed about the world and Ginko and so on (although it didn't resolve some things as such). The second series then basically goes around in circles, doing nothing much new with the things I cared the most about in the first series. There's nothing in it that I can point to and say 'yes, that was necessary, that changed or deepened my view of things', even though there were plenty of nice things.
Assigning fault here is hard if not impossible. The first series did everything right in terms of pacing and story selection, especially given that people had no expectation that it would be continued. The second series then has to work with the (remaining) underlying material it has, which is probably generally episodic in the first place, and it likely isn't in any position to significantly evolve or change Ginko's situation (especially if the source material doesn't). That leaves it pretty much stuck, with little left to do except tell its episodic stories. It tells them very well (cf) and it's not anyone's fault that they're less entrancing and engaging to me than finding out more about Ginko and his world.
I expect that this is a quite personal take on Mushishi as a whole. My strong impression is that most people who watch the show are far more deeply touched by the individual stories in the episodes than I am.
(I do find the individual episode engaging and often powerful, for what it's worth; they're good observations on people and the human condition. But to me they're just not as memorable and powerful as the overall story of Ginko and his world.)