I think Emet was exaggerating how much difference it makes. He says everything is divided, strength, stamina, intelligence, etc. but that's very clearly not actually the case, at least in so far as the 7/14 of the Source and the 1/14 of the First are concerned.

I think there may be a link between strength and soul, but not in a direct 'getting an extra shard gives your Fire IV more potency' sort of way.
I picture it as the soul being the pilot and the body is the means by which the soul physically interacts with the world. A sundered soul probably isn't strong enough to wield the powerful nigh immortal form of the Ancients, hence why they didn't survive the sundering. The other side of that though is that a strong soul piloting a mortal frame is still stuck with the limits of the mortal body they're inhabiting.