Let's see: French press or Moka (in my country we usually call it Greca)?
My impression is that French press coffee is usually smoother, regardless of the roast, variety or blend you use. I think, as an inveterate drinker and observer, without being a specialist, that it has to do with the moderation of the temperature that is achieved with the filtering in press, which is usually slower. Moka, on the other hand, passes through the filter at full steam and ejects jets of that boiling manna. It gives a denser coffee, since it literally drags all the substance from the bean.
I say here in this, my physical-chemical fantasy! 😆🙃

The truth is that if a friend gave me a choice, in my heart I would choose the Moka coffee, although I understand that the French press is more ceremonious and more appropriate for entertaining. I also know that if my friend wants to pay attention to me, I would let him use his French press and it would also be a great joy for me to give him that opportunity: I would explore the flavors, textures, aromas and I would surely have an interesting and imaginative conversation with this friend about the differences between both ways of making coffee.