As a musician I was kept pretty much in the dark about strings and how they affected the tone, i.e. the harmonic series of a note. The marketing spin is full of non relevant information and mis-information aimed at establishing a brand name identification that will cause you to willingly part with some cash to have "Brand X" strings that are oh, so much better than "Brand Y". Buzz words (easy to remember) take over and actual physical characteristics are ignored (hard to understand). Even highly intelligent musicians succumb to the dumbing down inherent in marketing. Obviously, I'm not going to get any endorsement deals from any string makers.
As a guitar maker in the old days before usable computers, it wasn't much different. However, now days anyone who knows a bit about what they're looking for can see for themselves what the differences are.
I'd like to address one thing that I believe is at the crux of the whole string thing. Stiffness. When a string is plucked (or bowed) it is set in motion. This motion is a complex series of other motions called harmonics. See my page on the harmonic series to understand this in more depth. The point I want to make here is that the stiffness of a string is inversely proportional to the number of higher harmonics that can manifest (easily) in a vibrating string. The more of these higher harmonics that you can hear, the brighter the sound of the instrument, up to the point where it becomes uncomfortable to hear. To put it another way, the stiffer the string, the fewer upper harmonics can be heard and the duller the tone will be. This is often referred to as a "strong fundamental" tone. It can be loud, and it can sound very deep. I've heard people refer to this as a "deep, rich" tone. In reality it is not rich at all, at least not rich in overtones.
Please note that I am not passing judgment on any type of string. I am just acknowledging that there are differences that can be understood. If you want a stronger fundamental tone, use a stiffer string. If you like lots of harmonics and a bright tone, use a more flexible string.
It's easy to compare stiffness of two strings, just hold them out together horizontally with an equal amount of string extending from each, I'd recommend about 6 inches or around 15cm. The stiffer string will withstand the pull of gravity and appear straighter. The looser string will sag more. Make sure you are holding identical gauge strings of the same note/position. Holding two high E strings of different gauges can also give you a hint as to what changing the gauge of a string will do to the tone of the instrument. Higher gauge strings tend to be stiffer, putting more tension on the top, resulting in a stiffer feel and louder volume, but usually at the cost of a few harmonics.
So why would I want to adjust the harmonic series by string choice ? Isn't more always better ? Guitars are funny things. They aren't all created the same. With factory made guitars, you get what you get, which is often a rather dead sounding box. A very flexible set of strings can help introduce some liveliness to the tone of such a box. There are lots of very flexible (and expensive) strings available now days.
Individual makers, on the other hand, can concentrate on getting a particular sound. That often involves thinning the woods more than a factory would and bracing it lighter. This makes the guitar more responsive. But more responsive to what and where in the audio spectrum ? A guitar that is too responsive can be really loud but really problematic. It can be a problem because the top/back and air resonances all favor particular frequencies and have their own harmonic series'. The more responsive the guitar is, the more likely it is that some of the harmonics of the strings will trigger odd resonances in the top/back/air. Given that the harmonic series is the basis for just intonation and the guitar is an equal tempered instrument, the likelihood of harmonic dissonance is strong. The results can be notes that never sound in tune, even when played alone, and notes that are overly loud but quickly die away. A stiffer string can help calm down these issues, although the tone will be duller (comparatively) the end result will be more listen-able and less stressful for the player.
Rest assured, the ultimate goal of every guitar maker is an instrument that is perfect. One that is loud, responsive yet perfectly in tune with just the right mix of harmonic overtones. Given the state of our knowledge, this is still too rare an occurrence and we don't give such guitars away cheaply. Even on those guitars, the harmonic mix can be adjusted by the strings you choose to use.