The Galaxy S8+ has an OLED screen. No monitor except an OLED TV or an old plasma TV used as a monitor will look anywhere near as good as it looks on your phone screen. On an OLED screen, each pixel is individually addressable and can be turned from completely off (black) to on. The colors are especially vivid, and the pixels can turn on or off almost instantly. By contrast, an LCD monitor uses a single backlight (tuned to an artificial white so the colors are not as vivid), and the LCD panel lets the correct amount of light through at each pixel. There is always some light leakage so blacks are really a dark grey, and the liquid crystals take some time to realign so motion will be a little smeared.
Why don't you list the model number of your monitor and we can tell you what drawbacks it might have? 10 years old is recent enough that it may be using a LED backlight, in which case the usable life of the monitor is probably around 20 years. But if it's using a CFL backlight, those tend to fade over time with a usable life of 5-7 years before reaching 50% original brightness. You could replace it, but it'll probably be easier to get a new monitor and demote this one to a second screen.