In Nights on the Sega Saturn (also available on PS2 in Japan), the core gameplay consists of flying around, collecting blue balls, and performing lots of stunts in order to get a high score. The game features a very pleasant art style (reminescent of the classic Sonic style) and best of all, in my opinion, the best soundtrack that Sonic Team has ever produced.
The short length of the game, and the simple gameplay may turn some people off (there isn't much to do besides trying to beat your own score). Personally however, whenever I play it, I usually go through the whole game 2 or 3 times in a row every time, because I find the gameplay so satisfying (I could say the same about Crazy Taxi, another short game with a through-the-roof replay value) and the atmosphere so good.
At the core, it's an arcade game. There is a simple story in the game, but the characters don't talk, and there are no cutscenes, except a short one at the beginning and at the end.

Now for the second game... well, I've only played through the first stage of Helen's story, so I can tell you what I thought up to that, but that's as far as it'll go.
The most positive thing I can say about the game is that they have at least not fucked with the atmosphere like they have in Sonic. The music is still very pleasant (and would feel right at home in a Sonic game, by the way, unlike what they actually put in Sonic games nowadays) and the character look pretty cool.

But as far as I could tell with my time with the game, there are 2 things that ruined it for me. First, as with Sonic series, the story does its best to get in the way. The cutscenes are way too long, and most of the dialogue simply feels annoying and pointless. This makes me lose all the respect I have for the characters. I don't care that those little guys are called Nightopians, I don't care that fusing with Nights is called "dualing" (or whatever), I just want to get on with it and play! The voice acting is quite bad and the dialogue seems to have been written to appeal to 12 years old who like reading fanfics on the internet (the same as with Sonic).
I don't remember if the scenes can be skipped or not, but even if I could, I don't like skipping cutscenes because I feel like I might miss some important information. It's the developper's responsibility to balance it out.
This should be an arcade type game, not a game that tells a story. In the first game, the intro was short, had no dialogue, and then you'd start playing without being bothered between each stage.
Perhaps they thought the game was too short, so they tried to make it seem longer by adding as many cutscenes as possible..

The second thing that bothered me was that the added missions to the levels. I don't wanna catch some stupid bird, I just want to be free to fly around and do stunts before the time runs out, like in the first game. As I said, I lost interest before I got very far (due to how lame the characters are because of the story) but I have no reason to assume that the whole game isn't like that.

This game certainly isn't as abysmal as the Sonic series has become, but when compared with the first game it certainly isn't anything special. It's a shame too, because in many aspects it's very close to the original, it's just too bad they had to add so much useless garbage on top of it.