I prefer the saw far from me, not in my legs, not in the space visited by my hands. It's less bulky on the saddle to go throw the limbs.
When the ropes tangle with the saw, it's less likely to damage the ropes, because the saw isn't locked at the saddle, it can move somewhat and warns you before you make a good pull to free the rope (thinking that's only a twig).
Only time to time, I wish to have a short holder, to avoid dragging the chain on the concrete, some stones or a roof.