Speaker Output for Subwoofer--Sounds Better

I find using the a neutrik subwoofer cable at the subwoofer input to speaker terminals of the amp/integrated amplifier sounds better than using line level or dedicated subwoofer out (dedicated subwoofer out on my primaluna dialogue hp integrated).

I know REL seems to like using speaker terminals as it thinks it gives the subwoofer some flavor of the amp. Other than that, I see very little out there on this subject.

I really prefer using my three integrated amplifiers with speaker terminal outputs to the subwoofer.

Does anyone agree, disagree or have knowledge on this issue?