If I read you correctly; if the subwoofer gave you too much bass or mid-bass, then possibly it was not setup correctly. You had overlap.
If your main speakers go down to say 42Hz, then the subwoofer should be set at around 35Hz to 38Hz to fill in below the mains; not add to the bass already present. A subwoofer will always integrate, if what it gives you is bass not already present.
If you play middle C on a concert grand piano and a small upright piano, they don't sound the same. The concert grand is much fuller and richer even though it is the exact same note. This is because the frequency spectrum of sound is much larger than the frequency of middle C. This is also why the same identical note played on a violin, oboe, or any other instrument sounds different. Speakers have no problem playing the high frequencies. The low frequencies are the problem.
A properly integrated subwoofer does not give you more bass; it makes everything sound more realistic and clear, by filling in the missing bottom of the frequency spectrum you hear with live music.
