You answered your question already. Your research showed both ways work for people. Now, you have to do the work.
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I found letting the speaker do as much as possible and the sub do as least as possible is a much better sound.
The sub wont sound as good as the speaker in most cases.
So keeping it to a minimum is better in most cases.
Mt10425 is correct, you have to try it both ways and let the voices in you head tell you which one to live with.
Unfortunatly, my voices never shut up.
I agree with the above comments, and will add that I prefer my speakers running full range and sub to augment.One advantage to this arrangement is using the amp which powers th speakers to also power the sub (even if you have a powered sub) so the same amp is running all. IMO this arrangement leads to a more uniform sound.
In my case I'm very satisfied with the bass my Dyn C1's can produce but want them to sound deeper. I run them full range and crossover at 32hz. C1's run 45 to 22khz. When I cross over higher the mid bass sounds bloated and because it adds to what the C1's do I loose the deepest octaves.
That being said when set up properly (phasing) the sub sounds as good as the speakers. FWIW I have a Rel B3. I will admit with Rel you really need to get a real cable and not use the stock aluminum one that comes with it.
I imagine it comes down to how well your particular speakers handle the lower part of their range and how well the sub handles the upper end of its range. Which method works better probably depends on how those two factors combine, which goes back to the others' comments that there's no absolute right answer and there's no getting around individual experimentation in this instance (as in most in this hobby). Be interested to hear what you find since I may be in this situation as well in the future.
If you run your mains full-range, and assuming they have bass response to at least 30Hz, they may very well improve bass smoothness in your room. The more bass sources you have the more room modes are generated (dips and peaks in the perceived output level in the room). The more modes you generate the better they average things out.
With some speakers, especially those with relatively small woofers crossed over well into the midrange, relieving them of reproducing the bass frequencies may improve the overall sound more than increasing the number of room modes, especially if you have the flexibility to place the sub for best bass response, or you can use multiple subs.
I've tried several different alternatives in my system, and I'm currently running the mains full-range, but with a reduced bass setting on the so-called contour switch on the speakers, and I use a 120Hz low-pass filter on the sub, with appropriate equalization to cut some peaks. I also had good luck with a 60Hz low-pass filter with a shallow 6db/octave slope, and an 80Hz high-pass filter for the main speakers. I moved away from using the high-pass filter only because the sub's input was overloading on some passages, and distorting the feed to the primary amps.
In the end I think bass at my listening seat is best with the mains running full-range. Because my mains reach down into the sub-20Hz range it's like having three subs in the room.