not a linguist. I was just wondering if the degree of robustness of a language to environmental noise is somehow measured or studied. I presume not every language is equally robust, right?
This is a currently non-existent but potentially interesting specialization in linguistics. The design of the experiment would not be very difficult: make good quality recordings using a head mic, standardized recording parameters and multiple speakers, speaking normally (according to norms of that culture, which is the main thing that matters) – don't normalize amplitudes (since that would obscure a feature of interest). Then overlay environmental noise of differing characters, and see what the effect is on listener comprehension. If Bella Coola turns out to be harder to hear than Cantonese, Bella Coola speakers can adjust by talking louder, so there's no insurmountable problem regarding noise.
Apart from cultural norms regarding how one should speak, a language like Hawaiian is probably one of the most robust against noise because it has only open syllables and a rather restricted phonemic inventory, so less chance of noise overriding the signal. A language with significant consonant clusters and lots of consonant types would be most at risk: candidates include Berber, Kartvelian and Salishan languages, Polish and Mongolian. In the case of Berber, some of the languages have epenthetic vowels and others don't, where the vowels can make the individual consonants more audible. Another possibility would be languages like Vietnamese and Hmong, which rely heavily on phonatory differences on vowels as part of their tonal system (vowel phonation contrasts are not very robust w.r.t. noise).
In the mathematical theory of communication, which is an enterprise of engineering mostly electronic, noise reduction, detection and correction of errors, robustness (to use your word) under conditions of noise, all these are very important, maybe even the most important issue in the human designing of engineering artifacts (codes) to facilitate machine communication.
But, for whatever reason, all that very important research, while discussed philosophically by intellectuals in an informal manner, never really had a discipline transfer to linguists. There is surely some research into confusion of phonemes and other phenomena within particular languages, but I don't know of much into comparing different languages.
This sounds similar to comparisons of language length: the size of a text that has been translated into a number of languages, and which is the shortest and which the longest. There may well be succinct and, likewise, verbose human languages but the experiment to do so will be difficult because of the bias and artifice involved in both human composition of narratives and in the translation process. Average document length is actually one possible technical metric for comparing coding mechanisms so this is not just an analogy but also one very narrow example of what you are looking for.
So to your first question, no, I don't think there is any established technical literature (or much of it) that experimentally compares spoken language and content transfer under noisy circumstances. I could easily be wrong; it's just that linguistics, despite being a natural science, is not as interested in experimental methods as say psychology.
To your second question, very informally I would guess that it all depends on under what context you're comparing robustness. If you are comparing yelling but/sell commands in a noisy stock market environment, one could experimentally determine which language is more accurate, but still allow that there may actually be either 1) No significant difference, or 2) a statistically significant difference that in the long run has little substantial effect.
I think there are too many social variables to account for before saying that one human language is more accurate under noise than another.
It's been said that the Piraha language could be understood even if it's just whistled in the air. If that's true, it's very robust to noise.