Everyone has their own set of preferences when it comes to the attributes they find attractive in objects. This holds true for the physical beauty we see in things like a human face, the shapeliness of a sculpture, the design in a painting, or the graphics in a videogame.
The Shenmue games on Dreamcast impress me more from a visual standpoint than Metal Gear Solid 2 on the PS2. What strikes me first when I compare the two is how much more detailed and how much more clearly I can see the world of Shenmue. In Hong Kong and Kowloon, I can see buildings towering overhead all around me, the streets lined with stands and storefronts, the bins stocked with a wide variety of vegetables and merchandise, and upwards of thirty distinctly detailed characters on screen simultaneously walking and shopping about the marketplace. There's a full view distance of the environment, with no fogging/obscurity or environmental draw-in ever. In smaller environments like Scarlet Hills and Guilin, the texture resolution and integrity is turned up a notch, leading to just breathtaking depictions of nature - rich layers of foliage, sharp detail on gravel pathways, and complex striations on rocky surfaces. The way the world soaks up color from the sun, like when late afternoon brings a global, orangish glow to everything while elongating and bending character shadows over the undulating terrain, never fails to capture my awe.
To realize these kinds of environments, the Dreamcast is pushing an impressive amount of texture variety and quality while handling all sorts of effects at the same time. Shenhua's dress ripples gracefully in the wind, subtle movements of her (and any character's) face can represent a whole range of expressions during real-time conversation, the behaviors of shadows are handled incredibly over even corrugated surfaces, and crowds of NPCs from an available cast of over 1000 uniquely skinned and clothed characters can wander into view at any time. This kind of micro-detailing is set against an environment that I find second-to-none among videogames - there is no plague of "sameness" when you look around Shenmue's world. The textures on the paths you walk throughout a neighborhood or on the walls of adjacent buildings feature surpringly little repetition, each storefront at each building is fully modeled with unique detail, the shops all have their own signs and look, the canopies covering the grocers' stands sport separate patterns/designs and color schemes, etc.
It's this variety of surface detail on objects within a single area that really brings this world to life for me visually. Things are clear and have individuality - one end of a street looks completely distinct from the other end. There's no particular overall color scheme or styling - it's like a sensory overload, and I find it quite intoxicating. That's not to say that I'm ignoring some of the often glaring visual defects of the Shenmue games on Dreamcast. The NPC pop-up (fade-in, actually) is jarring at times, and the slowdown in Shenmue II can be annoying in a select few areas. Texture alaising is also a particular nuisance in Aberdeen and Wan Chai. While visible, these defects mostly get drowned out by the copious detailing and lush colors in which the world is draped.
Clarity and distinction in graphics are what immediately jump out at me, and they have a strong influence on my overall impression. The Dreamcast and Xbox have a big leg up on the other consoles in this regard. Because almost every game in their libraries can output progressively, I can play them though a VGA Box. This is a huge visual trump card to my eyes. Honestly, playing Soul Calibur at home on my Dreamcast on my 19" monitor impresses me a whole lot more than the comparatively dull display of the Soul Calibur II machine they have at my local arcade. Everything is so buttery smooth, clear, and vibrant on my monitor, but the extra geometry detail and effects of the sequel are lost on me because they just don't stand out. (I'm hopeful Namco will allow the home console conversions to support a non-interlaced output.)
Visually, I'd pick many Dreamcast games infront of some of the best-looking games from other consoles if I'm playing through my Dreamcast VGA Box. For one, as a minimum, the Dreamcast fills the entire 640x480 display. With quite a few PS2 games, I get a visible black border from the game being rendered into a slightly smaller screen space (Probably the 640x448 games... Actually, I'm not certain the exact cause for that as my TV has quite the exceptional visible screen area. One thing I'm sure of is that the image isn't as sharp as a standard Dreamcast game on those titles.) The VGA Box graphics also provide a fuller animation, as double the resolution data of an interlaced display is being sent with every update on 60fps games. The colors are amazingly rich and vibrant on my monitor, quite distinct from each other with no bleeding or loss of accuracy. Lastly, the dot-pitch on monitors is so such smaller than televisions. I actually do pick up on the appearance of pixels from a moderately-sized television display (35 inch and up) to some extent. TVs artificially stretch the projected image more than monitors, and the resulting picture elements are physically larger and more visible. If you're seated the appropriate, corresponding distance from a 19" monitor's display, it fills roughly the same view field as a big screen TV. The effect is fairly similar, and the added sharpness of playing the games on a monitor is simply eye-popping.
This wouldn't be such a big advantage for Dreamcast and Xbox if more games outputted full resolution at each update on the other consoles too. Right now, there's probably less than ten PS2 games and not nearly enough GameCube games that are VGA compatible.