LFE vs High-level subwoofer connection, for FIDELITY

@bartsw im looking at an anthem SA35 to get Dirac live in a system, to compare to my reference system, Cuz Dirac works so damn well on my Onkyo AV. BUT audiophiles usually scoff at that. And idk any balanced component I could put in my component stack, that has room correction. Minus $10k+ preamps like the Trinnov Amathyst that have room correction 

@toddalin that logic would then affect both connection types, right? So obsolete 

If you put the sub input on the main speaker output, the signal goes through a preamp, then the mains power amp, then the sub's power amp.

The other way it goes through a preamp then the sub's power amp and skips a stage of amplification.  Not the same thing.

The "extra fidelity" from speaker level connections is some extra foolery propagated by the REL guy...

If the preamp has xlr pre-outs and the sub takes xlr input...I would go with those and call it a night...If that's not possible, use the rca preouts and don't worry about it.

I'll eat my hat if anyone on this forum can tell the difference.

What subwoofer connection method offers higher fidelity, and why? The LFE, 75 ohm unbalanced RCA cable. Or high-level, speaker wire to the binding posts of the amp.

Subs with built-in dsp can add a tiny bit of lag....it was discernible on some older subs with built-in dsp..if you didn’t have the ability to delay the main speakers to compensate (as would be the case in a purist rig). It had gotten better these days.

Does one add to "lag time" and does this even matter?

@kr4 I’ve got the same experience as the other responder. My sub has eq knobs, low pass filters and room gain filters on the back panel. So my bookshelves roll off at 50 hz, so I set the sub to 60 hz and under. Even on high pass, the sub filters it