Completed the sequel yesterday, and my initial impression got confirmed in the sense that I think this part of the remake is actually better than the original. It's not an all-out improvement, but just being able to move around freely immediately improves the overall atmosphere and sense of place. I actually never completed the Wii game because it was such a distant, almost superficial experience and the intrusive UI torpedoed any sense of immersion. So I can't comment too much on narrative or gameplay differences*.
Narrative is a good key word though because it just barely has enough puzzles to make me remember writing that word here. I think it's two or three in total, combined with a couple of minigames – ultimately though it's very much running around and talking to people, in a similarly glacial pace we've seen from the likes of Shenmue or Life is Strange. Unlike the former, it's a very guided experience and it lacks the decision-making process of the latter, but for what it wants to be (some kind of YA mystery anime-style story) it works. I really enjoyed going through it, it's an almost cleansing after-work kind of game. Weird description, but if you are out and about for a day and get home and just let yourself fall on the couch/bed? This game is that feeling.
*I did go back to watch some videos of both the first and second game on youtube and they really changed a truckload of things. It's definitely a proper remake in that sense because there was no stone left unturned, for better or worse. The second game even completely rewrites a major 'antagonist', if you want to call them that, while reshuffling and removing some other NPCs that were just one-off exposition-blasting cannons. They also concluded an arc that was previously left open in preparation of a spin-off Cing never got to do before they went bankrupt. They definitely put more effort into this than meets the eye, even if it might not be immediately apparent due to how low-fi the technical side is.
The best way to experience these games then would probably be playing the DS original of Two Memories and then the remake of the second game. It's too bad you can't really do that because they mixed both into one in this, but the homogenised approach does have its charms, too, even if an optional choice would have been welcome.