I have abused Mathematica since version 3 and right out of the gate I will say that the Notebook interface remains unparalleled compared to other platforms: MATHLAB, Python, R, Stata (of which I have working experience). Although Livescripts have been a welcome addition to MATLAB, I still prefer Mathematica as a comfortable graphical interactive workspace. I have only used MATLAB for the past 3 years, so my experience is limited. I find working with matrices cleaner in MATLAB and the documentation/implementation of higher-level matrix functions more informative (and easier to relate to textbook instruction of Linear Algebra). (I have, respectively, a love-hate relationship with MATLAB and Mathematica when it comes to pre-multiplying a matrix by a column vector.)
In data analysis: I like Mathematica’s handling of statistical distributions, but I find its statistical modelling limited and awkward to extend beyond Master’s level applied statistics. MATLAB is has a much richer implementation and output. Mathematica’s Bayesian capabilities (including various MCMC offerings) are no where to be found. (I recognize this last statement is not literally true; but it may as well be because efforts to create Bayesian models for undergraduate-level applications requires considerable competence (as indicated by the coding examples offered by Community contributions). MATLAB has more extensive statistical modelling offerings but likewise gets complicated, but possible, to use for Bayesian stats. I find Mathematica’s handling of temporal data (and date/time functions) and time series analysis superior to MATLAB. And when it comes to data munging, I also prefer Mathematica (due largely to the ease of intermediate display of data in the Notebook). I do not have experience in MATLAB with stochastic processes; but the Mathematica implementation is very impressive and enjoyable to use.
I prefer to work with text data and strings in Mathematica and my limited experience with MATLAB suggests that Mathematic’s string manipulation capability is superior.
Neural networks: At the moment, my knowledge of the Machine Learning implementations in both environments is limited; but I prefer MATLAB and my early experience suggests autodidactic ingestion of Deep Learning and Neural Nets is more approachable and rewarding in MATLAB. The Deep Network Designer in MATLAB is a superior environment for building and experimenting with NN. I have no direct comparison, but I find MATLAB faster, especially with the Parallel Computing Toolbox.
I find MATLAB’s Regression and Classification Learner “apps” superior and much faster (especially Gaussian Process modelling) to Mathematica’s Predict and Classify. However, if I supplement the latter with the Find… family of commands; I think I would lean to Mathematica. The issue here is more my knowledge as a User (ease of use and immediate functionality often become less attractive as the user’s capability and the problems’ complexity increases; and I am at the lower end of the scale on both of these considerations).
I have not used MATLAB long enough to have an opinion on its evolution. But Mathematica has gone through significant changes. I had the impression that Stephen Wolfram took his eyes off the ball between, say v8 and v10, but has returned to press for a strategic and consistent language-level implementation. The vision of this endeavor is breath-taking. For example, the Entity Framework design is awesome, if awkward. And more generally, I find the improvements are impressive but sometimes difficult to grok and work with without a lot of fine tuning. As well, it seems some of the implementations run out of gas before they get to a full maturity (where they are worth the time and effort to learn in detail and by rote). I would suggest Wolfram’s database access and instantiation in Mathematica’s knowledge representation and access framework as an example of the latter. In my experience Mathematica’s database access is superior to MATHLAB. The impressive RelationalDatabase, EntityStore, EntityValue, EntityClass, and family of …EntityClass commands are so full of promise. But, for me, they wander into a jungle of syntax that is so difficult to get right that I fall back to what I did five versions ago with SQLExecute. (My bad, I just found the “Relational Databases Quick Start “ Technote which is “New in 12.0”. But I think this underlines my point. I had given up trying to master the Entity Framework and SQL because the implementation and documentation were incomplete in V11. And, I will get back to you when I finish what looks like the longest Technote in Mathematica. But I will not mind if the implementation does meet the promise and my expectation). (By the way, I feel this is similar to @Szabolcs point: “too many operators and the need to remember their precedence never bothered me, but I agree that one must have discipline and exercise self-restraint when using operator forms. I think I use them less, and them more and more restrictively, as time passes, not more.”
I will not address the Symbolic capability here. I have made primitive use of MATLAB’s Symbolic Math and Partial Differential Equation Toolbox but I would NOT give them a moment’s thought if I wanted to produce something akin to Nachbar’s “Epidemiological Models for Influenza and COVID-19” Notebook (https://www.wolframcloud.com/obj/rnachbar/Published/Epidemiological%20Models%20for%20Influenza%20and%20COVID-19--full%20version.nb).
Both platforms are now so rich, extensive, and complicated that they require a support Community and third-party publications. In terms of texts: I find MATLAB has out paced Mathematica and that it is easier to find reference works for MATLAB. As to community support, I find Mathematica Stack Exchange particularly good. But, in my experience MATLAB’s Community support and offerings is more active and richer than Mathematica’s.
As to the Philosophy, I think, with Stephen Wolfram actively at the head and pushing his Company towards a strategic goal with adequate and consistent documentation, Mathematica holds a clear edge in vision and thematic endeavor. And it does feel like a Computational Engine with scary, almost unmanageable power. Something well-placed in a Consulting firm versus a manufacturing plant. MATLAB, on the other hand feels like a comfortable enterprise engineering application platform, squarer and more manageable.
I work with Mathematica everyday (as a hobbyist) but I enjoy some autodidactic exploration with MATLAB. I would accept either as my working environment in whatever Company I worked for; but when I got home at night I would prefer a fight with Mathematica’s syntax (and the eventual reward) than a dry serving of MATLAB.