Let me be frank - I don't like to think of this as a sequel to the original.
What I liked was basically just the return of my favorite characters from the first season (other than our MC, but I'll discuss that later).
[kind of spoiler territory]
At the beginning, I thought every season would simply be the antics of a new master and butler, with the previous season intertwining within the narrative. Unfortunately, it wasn't nearly as good as I expected. Our new pair wasn't nearly as dynamic as the original and the ending was...something.
If this was a standalone series, I might have liked it slightly better, but not after such an interesting first season.
There's my two cents.