I'm only on the third case of 2, but so far:
The two games are definitely intended to be a sort of package deal. The first game sets up a lot of plot threads and foreshadowing for what's to come, and the second game largely follows up on all of these. It's a bit like a lighter version of Higurashi and Umineko with their Question and Answer arcs.
If you played Layton vs. Wright, these games almost feel like a more Phoenix Wright-ified follow-up to that. Aside from puzzles obviously, many gameplay mechanics were carried over from there and a lot of the character design feels like it would be right at home in a Layton game. Not to mention the whole British thing too, of course.
In many ways it feels, tonally, like Phoenix Wright 1 and 3 bundled together. You can definitely tell it's the same style of writing as those games too and doesn't have *as many* contrivances and general aping of the originals as the newer Phoenix Wright games directed by the B team have.