More knowledgable users will surely chime in shortly, but from what I understand, there's two sides to this: tone and playability. A bit counterintuitive maybe, but from what I understand thicker strings have more overtones, while thinner strings have more fundamental and more sustain (?).
Bigger strings = bigger tone is definitely a myth.
I disagree with the previous comment that says you lose clarity with lighter strings. If anything, I find it to be the other way around. In my opinion/experience, lighter strings sound better. Brighter/clearer, more musical, better tone.
Tanner5382 has the right answer, here. I've only read up through post #10 so forgive me (or, not

) if I am regurgitating what may have already be said here.
Think about how a solid bar of metal sounds when "plucked" compared to, well, a typical bass string.
Another way to actually hear the difference is playing long notes on an E string. How does the tone/sustain/etc. sound when you finger the string at the 12th fret compared to the sound of the open string? As one progresses up the fingerboard, that string is becoming, more and more, like that solid bar of metal.
Overall, lower/thinner gauge strings ring out better/longer and have more overtones/harmonics than higher/thicker gauge strings.
For many years now, I much prefer lower gauge (and tension) strings on my basses. No loss of tone, or anything else for that matter, IME. If anything, it all sounds better to me, plus the lighter touch I use is an advantage for me.