Well, sure the player and the bass matter a great deal. Still, holding those constant, which I took to be what the OP meant, I think some generalizations about strings can be made. Generalizations, not absolutes. Thus, my answer about the Evahs. Of course, two different basses, with two different players, and two different setups could overwhelm any string generalizations.
Yes, you got me. For you, on your bass, with your hands, arco or pizzicato, and otherwise every other variable controlled... what strings do you put on for the big sound? It could be fat, it could be deep, it could be low tension, it could be quiet, it could be high tension, it could be anything. I guess in mind my at the time of posting I'm asking a very basic question, asking for something practical, not just bulbous. After, even if you have more than one bass, you can only be in one place at a time.
I do understand how the bass has limits, is not infinitely deep, the resonance of the A string is a good marker... although a good E gives you much more reach downwards. I'd like to try and find a way to maximize that. Bass waves a exotic in a way, and I get grea joy in discovering their natures, having that as my duty... the bass can produce all frequencies, and people like Rabbath have shown us that a minimal action can produce these fundamentals as well - it's not about strength, the instrument is big for you, the string is long for you, etc. So how does one get a focused enough sound, which is usable, agile, not just big....? With my experience on Corelli 370M set I've seen that the bass is indeed only so deep, in that it can sound more focused and 'comfortable' (to me) and bigger with actually a lighter or looser set up, and if you push it to be bassy too much the sound can be harmed... after awhile you end up augmenting "mid" ranges, which may be good, focused. Certainly, if the action gets too loose and free then it can just sound mushy, uncentered and lacking definition... this is a good thing in a way, because then you may learn that the focused sound is you, what you do at the moment, and then you can be free to play what you want, it's crazy, but some people think a focused sound requires something - it doesn't. If you pluck softer or louder, the sound is the sound. Same for the bow.
So I use solo obligato strings tuned to orchestral ptich because I realize that playing small on the instrument makes it sound bigger, and because my left hand is messed up, weak. I went into playing thinking you need to push a certain amount to get the bass to speak over the other frequencies, which is true, but not as extreme as I was taught. In other words, that harmonic became fundamental with time when I'd play with insufficient wieght - a world-changing discovery for me and my stiff-ass bass. Playing on Corelli370M felt good, but I thought, let me keep the low tension, the low action, the ease of playing, the response, but get more body, more bass, more warmth, more gauge... I went with solo because it seems closer to 370M, smaller, than orchestral tuning. For sound, for my hand. Now I've seen how weightless one can play and still be profound, and I can imagine playing with low action, so I guess I could use any string now, as long as I can finger comfortable.
PB+J is right about long tones, I think, being able to have a strong left hand, to be able to get the fullest vibration and keep the string down - this is no small task for me. Now I've been using an orchestal E string and I see how it's big but not choked, going with the solo strings - and obligato is loose as a brand, I feel. I like to have that action, that clearance and still be able to play comfortably with my left hand, the sound has definition but it's really blending, not twanging or cold or super focused. And yet, I'm wondering what can be done to get more, big and bass sound and yet I feel free - a big string does not have to translate into choked sound, or dark sound. So the bass puts out a blend of frequencies and we have to adjust this palate. It's a bit of a compromise, you know, so that when we go for a bassy sound we can drastically lose treble, etc., falling into a response that blasts the bass over everything else, or vice versa.
So I think, somewhere in between there's softness, complexity, brillance, playability, response, and definition, strength, expressive range, depth, weight, etc. The bass has a fixed size and so it's not right to think that it can sound great no matter how big the string is, to me, and everntually there will be a lose of tone greater than the gain... fundamental vs. harmonics, simplicity vs. complexity... maybe that's all wrong. I'm not just trying to get the most out of my instrument, which is a fair thing to try, but I'm also trying to get the lowest frequencies to be as obvious as the others, if I want it, to be consistant, to be even, blah, blah, etc., etc..
And of course it's different to everyone else, never mind the instrument, just considering the difference in hearing, in perception... what's the thing people grab onto, what the loudest part? I'm dreaming of something where that string core sound is in balance with a fundamental so deep that the player and listener can travel together into a sound range that's so low and clear and focused and accessible that one forgets everything - that the bass sounds this way or that way, that it's weaker on the E than the A, typically, and eveness and agility are matched. I may be close with the setup I have now, more than I know... I really like it.
Obligato seem good for their looseness, and their tone is unique. I feel like that looseness gives lows, softens the core sound, creates some highs, some mellower edge. The gauge and tension pushes the whole thing to be heavier, more definite. Starting with the solo gauge means I'm more within the easy zone of the instrument, and then the E just sounds more, not strident or forced. I certainly mean to go into the heavier strings, put back on my Original Flexocors, and exploit the action to a full range. I feel something's gonna be fun, going that direction... lower action, more response, less weight, more brillance, and the heavy sound. They maybe the answer here, or more like it. So what am I doing typing... Because when I soften the action I lose that fundamental and get more of a feeling of midrange and fluid sound. (This is hard to talk about I can tell from everyone's post. At least I'm still left wondering.) The mid tones and warmth and edge and fundamental and everything else need to balance; the textures, the frequencies. An overall tone needs to be well rounded. We can come to generalizations, theories, but it's not the way for everyone. I'm gonna put on some Evah Pirazzi orchestra in March 26, since then I'll have had the Obligato for a year. It may be so much simpler then. I've had the Flexocor 92's and they were good, somewhat tight, but focused therefore. The may sound fuller with lower action, softer, more flexible, but yeah. It's a personal quest, I know. Thank you for response. Keep on until you're there.