i am currently using both methods, line level IS BETTER, so you see someone using both, and have so for more than 4 decades is commenting.
Again, you would be hard pressed to hear a difference, but line level IS the superior method, it's not debatable. One method sends exactly the same signal through shielded cables to both amps.
The other method sends the signal to one amp through shielded cables, amplifies the signal hopefully as accurately as possible, then through unsheilded speaker wire into the mains, branches off into circuitry to lower the output, then sums the two signals, through a low pass filter, etc, then amplifies THAT signal for the sub driver, makes a lot of sense to me, NOT.
This is why it's not recommended in the high end by every other manufacturer othet than REL's marketing gimic, and even they offer line level inputs. I wonder why if they truly believe their own hype as any amp will work with high level inputs.
So let's see Rel put their money where their hype is and eliminate line level inputs from all their designs.
I don't know how many times I can say it, but you are presenting only one side of the argument. Pretty much any time you represent anything in audio as an absolute, you are not correct.
The tradeoffs are exactly this:
+ Line level is potentially cleaner because you bypass one element in the audio chain (the stereo amp)
- With line level, the sub is seeing a different signal than the main speakers, because the sub is being fed by the "preamp only" and the mains are being driven by the preamp
and the stereo amp
The only way that the stereo amp being in or out of the signal could be totally relevant (as you are trying to say it is by completely ignoring that element) is if every stereo amp in the world sounded exactly the same and was perfectly neutral. I seriously doubt you believe that is the case with all amps.
I've already given you examples of a SS preamp and a tube stereo amp -- with line level, the sub would only see the solid state preamp output --
the sub output would not have any characteristics of the tube amp (which is obviously different than the main speakers that ARE driven by the tube amp and preamp). You cannot argue they are same because they clearly are not at all.
The other example is that any "interaction" effects between individual stereo amps and speakers would be automatically be reflected in the sub when using high-level inputs, but interaction effects would be completely lost with line level. Here are some more: If the stereo amp was at all non-linear anywhere in its gain curve, or if its curve flattened sightly at very high volume levels, the sub would always remain perfectly balanced with the mains with speaker-level connections because the non-linear gain would be reflected in both the mains and sub in lockstep (while the sub level would not remain balanced with non-linear gain using line-level because the amp is not in the loop). Your own statement that the stereo amp "amplifies the signal hopefully as accurately as possible" is another example, to the extent that a given amp isn't accurate or neutral, the sub will remain in lockstep with the main speakers when using speaker level (and will not be uniform with line-level).
The goal of the sub in 2-channel audio is to be a seamless extension of the mains, so having the signal to the sub always be in exact lockstep with the signal sent to the main speakers is a good thing -- but that is also subject to the potential downside of having an extra element (amp) in the signal chain to the sub. Neither approach is guaranteed to be better or worse.
The rest of the stuff about noise and summing signals is inaccurate and a wash (in other words, either connection could be better or worse depending on circumstances). All of the stuff about summing of signals and the low pass filter for speaker level are exactly identical for both connection types. Both line level preamp left/right output and speaker-level left/right output are full-range stereo signals, both need to be summed for a single sub and both have the exact same low-pass filtering. If the preamp being used has a mono sub output, the summing is done within the preamp (which is a wash with the sub summing left/right). If you are running two subs -- left goes to left and right goes to right -- there is no summing for either line level or speaker level (though the sub will still sum the signal with the empty RCA or empty speaker wire).
As far as noise differences between the connection types, it is far from absolute which one is best. Like everything else, it's situational. The signals in line-level are very low-level signals which are much more prone to interference than the much, much higher electrical signals in speaker wires. That is exactly why line level uses shielded cables and is exactly why shielded cables are not required for speaker cable. Whether line level or speaker level connections are affected more in a given system will depend on equipment and on what specific noise sources exist in that environment. Because the signal levels are so low, line-level is probably more likely to be affected by interference than speaker-level -- but either could happen, and which connection type has more noise would depend entirely upon the owner's individual environment (equipment used, cables used, cable routing, power cable routing, local noise sources, etc).