@clio09, I think of bass reproduction in terms of leanness vs. plumpness. I’ve worked some with upright bass players, so have heard them up close in all kinds of acoustic environments. I have also heard them from the audience side, both unmic’ed and mic’ed. The fault I hear in it’s reproduction is that of making it sound too "round", not as "stringy" and "sinewy" as it sounds live. In person, an acoustic bass sounds like it is part of the string family in an orchestra, not that different from a cello, just playing lower notes.
As for electric bass, I use the sound heard by the playing of bassists in my own situations (Fender of course---Precision, Jazz, and Telecaster basses, but also Gibson, Guild, Danelectro/Silvertone, Hofner, and even the awful Rickenbacker ;-) as a reference, but also that of Joey Spampinato (NRBQ)---whom I have heard up close in a small club (The Roxy in L.A.), and John Entwistle (The Who), playing his original Precision at The Carousel Ballroom in San Francisco. Spampinato has the ability to make his Silvertone sound like an upright, coolest thing I’ve ever heard! Entwistle had the most massive bass sound I’ve ever heard (awesome!), with lots of staccato attack, but it was still not "fat". He was a GREAT bassist! I sure would have liked to see and hear James Jamerson live.
Brian Ding of Rythmik and Danny Richie of GR Research speak of a woofers ability to stop quickly when the signal ends as a major requirement for good bass reproduction; the lack of "overhang". There is also "overshoot"---the woofer traveling just a little past where it "should", smearing the bass in terms of it’s transient/temporal characteristic That’s as good an explanation as I’ve heard.
But all the above is about the reproduction of the bass as an instrument. In regard to over all bass balance in home hi-fi systems, rarely do I hear reproduced music with the bass weight and heft I hear at live music performances. Live music is much more "physical" than is reproduced, that physicality mostly low frequency in nature. A large part of that has to do with SPL, but also the size of the rooms music is performed in. Large venues support longer wavelengths (lower frequencies) than do smaller ones, and sound very different from our listening rooms. The final frontier in music reproduction!