I've read Carbon steel takes a sharper edge and is a tad harder than HSS, but less tough. In theory Carbon steel should be fine for hand taps, but the steel is rather brittle and likely to snap if the tap goes in off-centre or is bent by the operator. Bottom line HSS takes more abuse!
With care carbon taps and dies are OK, and may be better for Brass when new. The extra toughness of HSS is good news, but it's main advantage is it stays hard up to 500 or 600°C for machine cutting, unlike Carbon Steel which softens at about 150°C
Most of the cheap carbon steel taps and dies I bought in the 70s are still fine – their inferiority shows up only after a fair amount of use. The small much used sizes have all been replaced!