Typically high carbon steels will have better edge retention and wear resistance. The trade off is of course they're a "carbon steel" and more easily risk corrosion. Stainless steels have the addition of chromium and other components that give it the "stainless" quality. Depending on the user some might not be comfortable with tool maintenance or may be inclined to forget their tools outside in which case stainless would be better to own. Stainless tends to be more expensive than carbon steels though partially because of a more complex production process but more so being harder to machine and work. To put this into perspective try sharpening an old slip joint on a simple whetstone or Arkansas stone. Then try sharpening one of those modern budget kitchen knives you can find at walmart or what have you. The kitchen knife should be substantially harder to sharpen. Because of this for a carbon steel and stainless steel at the same price point, the carbon steel will almost always performs better. That's how the conception arose that using carbon steels are superior or better. Don't get me wrong though. You can get stainless tools far outperforming many of the carbon steel tools commonly used but the production cost and consequently sale price would be too high. Looking at the American Bonsai site they use "400 series stainless steel." Its probably 440C or 420 commonly found as a simple stainless in pocket knives and kitchen cutlery. For comparable money you probably could get a better performing carbon steel tool which is my preferred option unless you have big rust concerns. Looking at a popular maker of Japanese bonsai tools, Kaneshin, they use blue, white, and yellow paper steels--from highest to lower quality in the order listed. The blue and white steels especially are really nice stuff and have great qualities. Their tools are similarly priced.
That said don't pick tools only based off what they're made of. You can use fancy expensive materials but if the heat treat is done poorly you end up with a poor tool. So buy your stuff from someone with a good reputation--chances are they have their production process sourced well or heat treatment dialed in.
I chose SS not only because of the corrosion resistance, but, Masakuni puts a special coating on their SS tools that requires nothing more for clean up than a quick wipe with a wet rag. Before purchasing my Masakuni's I had a few other decent quality Japanese tools that were carbon steel and even in my dry climate of 0-7% humidity on average, and with 3-1 oil, it didn't take more than a couple of weeks for them to start showing signs of surface rust. SS only take 60 seconds longer to sharpen on tools like this than it does on carbon and I can definitely live with that
