I use spindle gouges from Thompson Lathe Tools for my pen turning by hand on my wood lathe.
I use carbide end mills / engraving bits (various types) for my carved core blanks that I make with my Digital Ornamental Lathe.
I use HSS tooling in my metal lathe for stuff I need / want to do on the metal lathe.
Learning to sharpen / use the tools you have is more important than what tool you have.....unless the only tool you have is a shovel (or something like that). At least that's the way I look at it.
Ed (who does not sharpen carbide end mills / engraving bits....but who wishes he could)
For wood I use a spindle gouge to rough turn and then depending on the wood a skew or carbide tool rolled on edge for final shaping. For acrylic I use a spindle gouge. I can get a surface that is ready to sand just with a sharp gouge and light touch.
Nearly any tool can be used effectively. Just practice with the tool of your choice.
My choice for 15 years was a roughing gouge, for the last five, a skew. But, I can turn a pen with any tool you want to see, as long as I am allowed to sharpen it the way I want.