Carbon steel or stainless steel knives?
The advantage of stainless steel is quite obvious: it doesn't rust. Or at least, it doesn't rust that easily. Any type of steel can rust in certain conditions, but under normal circumstances, stainless steel won't. This is achieved by adding chromium, nickel and other elements to iron besides carbon. The ratio between these ingredients and the way in which the steel is produced determines how stainless and how easy to process or shape the steel can be and also the hardness the steel can reach. Hardening the steel is mostly done by (extreme) heating and cooling.
Cheaper types of stainless steel contain a lot of irregular carbides from adding the different components together and suboptimal heat treatment (kind of like lumps in a batter or dough when not properly mixed and kneaded, for those who are into baking). That makes them more difficult to sharpen and sometimes impossible to give a truly steady edge. More advanced types of stainless steel can be made to be extremely hard and smooth and still stainless, but because they take complicated processes and heat treatments to make, they are much more costly. Examples are VG10 (Kai Shun Pro Sho, Miyabi 7000 D), VG-Max (Kai Shun Classic, Kai Shun Premier), FC61 (Miyabi 800 DP), or even MC63 (Miyabi 6000 MCT, Miyabi 5000 MCD) or MC66 (Miyabi 5000 MCD 67) powder steel. Some of these expensive Japanese steels are now also produced more cheaply in countries like China, but they rarely, if ever, reach the same quality.
The beautiful thing about a carbon steel knife is that, because the steel is much simpler, it's a lot easier to make, heat treat, harden, forge and sharpen. Because of that, a simple but well made carbon steel knife doesn't need to be prohibitively expensive. It's also possible to grind carbon steel to an incredibly thin blade (Dünnschliff) without easily folding, tearing or breaking.
The biggest advantage to the end user, besides the edge retention, is the ease with which a carbon steel knife can be sharpened. Because of the simplicity of the steel and the fact that it has a minimal amount of irregularities it can be sharpened without much effort and can keep a proper edge for a long time.
The biggest disadvantage, if you can even call it a disadvantage, is how quickly a carbon steel knife can rust. It means you have to make sure to always clean and dry it thoroughly after each use, which takes a bit more of an effort. The knife will also show more and more discoloration after time and use, developing a patina. This is completely normal and actually prevents rust from forming on the knife. On top of that, it looks absolutely beautiful.
So yes, a carbon steel knife requires a little bit more tender loving care than most stainless steel knives. But if you're the type of person who doesn't take care of their knives, what are you doing here anyway?
Another thing to be aware of is that, before the patina has formed, certain foods can get a slightly metallic taste from being cut with a carbon steel knife. This should only last for a few days or weeks, depending on the use. Some users like to speed up the patina process by treating their knife with vinegar, mustard or a host of other substances. Some prefer a more natural process, where over time the knife will tell a story about every ingredient or piece of food it has ever cut.
Like with most tools, there are multiple good choices for a knife. Every chef or home cook has their preferences. Some will only want stainless, some will only want carbon, many will like to have both at their disposal. In the end, it's a personal choice with no right or wrong.
As a general rule (which obviously doesn't always apply): the harder the knife steel, the longer it will hold an edge, but also the easier it will chip or break.