There are a lot of factors involved in this, and I'm not sure I'm qualified to address them all.. but like Sam, I'll try to give and answer that is hopefully "better than no help".
To me, the biggest issue is the string diameter versus the string length. On just about every string, playing a note higher up on the bass will sound less resonant than playing the same note down lower on the next higher string (the best example is the open G note played on each successive string). We almost always choose to play those "A and above" notes on a higher string because the string gauge and length are better suited to making them sound better, and we want to sound good. However, sometimes we can't help it. The area I spent the most time with in this regard is using the E string to play the bottom note of a progression of double stops, as exemplified in the first minute of This video. I guess the best question to ask before going further would be, do the bottom notes of these chords sound any better or worse than how your bass speaks?
