Carbon steel is easier to sharpen and costs less, stainless has better corrosion protection. If you like shiny blades, stainless is what you want. If you're really cheap and don't care about shiny, then carbon may be for you. I have a lot of carbon steel kitchen knives.
Typically, there is virtually no difference in honing a carbon vs. stainless straight razor. Carbon blades are also capable if taking a nice mirror finish. More times than not, this issue boils down to personal preference.