I usually classify my VNs to the overall design and resolution of the game. After adapting to the 16:9 widescreen ratio, I find myself hard to return to original 4:3 ratio even though monitors and TVs all used that standard back then. VNs that are not 720 HD sometimes follow the 4:3 ratio. Even though widescreen displays and monitors were becoming widespread around 2005, most VNs did not become widescreen until 2010. So basically, 2010 is my cutoff point between classic and modern.
Another feature I use to distinguish between older and current VN is the way the game is presented on my screen. My laptop screen has desktop scaling to accommodate the 4K resolution. Newer games disregard the scaling while older games will follow the scaling (a 720 HD VN in windowed mode will fill most of my screen). It feels to me that the newer game will have a better engine and interface that will allow more animation and effects.
As for art and design, I believe the differences and evolutions may be due to the resolution and graphic performance of the game. With higher resolutions, the lines become more crisp and it is possible to add more detail and color to the characters and BG. Compared to older games, it seems less smudgy and blurry. In the older days, computers were also not that powerful and people needed to consider that.
As for story, story never gets old. Heck, there are even classic stories that have important values that are still relevant today. However, dated graphics and interface will make the VN a hard sell since these are two items players will see at first glance. For sound and music, I really don't see how it can be improved since few people notice the difference using high resolution audio.
The main problem with VNs is that there's always a bunch of new releases every month. There are many VN studios in Japan and some studios have different divisions and subsidiaries meaning that they're working on three games at the same time. With limited space in the press, attention is usually focused on the latest titles. The western market has only seen a tiny fraction of all the VNs you can buy in Japan and it's usually the better titles that are handpicked by the translators and/or the fans.
Last note: I believe the issue applies too to video games. There are many new games that come out every month and the only element that gets heavily publicized appears in the media is the graphics and the interface.