My preference these days is heavily biased toward a more toothy bite in my working edges - something that really only comes from a coarse or medium grit stone.
Years ago, I used to rely more on a strop with compound when I was doing more polishing of my edges. But if the desire is to maintain a toothy bite, then that'll only diminish with prolonged stropping. The edge will always become more polished and less aggressive in slicing cuts, if nothing but a strop is used to maintain it. I also tend to believe that even if one is careful to avoid the rounding effect from a soft substrate like leather or fabric on a strop, the edge will still get too drawn out and too thin on a strop to be durable for anything much more than shaving hairs.
I like the fine balance between slicing aggression and edge durability that careful edge-leading finishing on a medium grit stone provides. Any stropping I might do beyond that is always very, very minimal and is done using no compound at all. Just basically enough to remove any loose, weak remnants of sharpening from the apex and no more.