There are basically two types of typesetting programs: Those that show the end product as you go; these are referred to as WYSIWYG, or "what you see is what you get". (If you've ever used MS Word, then you've enjoyed the simplicity of a WYSIWYG program.) The others are non-WYSIWYG, which usually means that it uses a markup language, like HTML does. A LaTeX file, like an HTML file, bears little resemblance to the displayed version of the file. In the HTML world, a browser is a program that takes in an HTML file and interprets it to form a webpage in the browser. Yes, there are WYSIWYG HTML authoring programs, but if you want, you can make an HTML file in a simple text editor, which in Windows is NotePad, which is what I usually use. Now, it's clear enough that my webpages are never going to win any awards for their beautiful design or layout, and that's fine by me, but when it comes to my typesetting mathematics, I want the best output I can afford. Oh, and by the way, there are free versions of LaTeX for all (or at least most) computer platforms.
Let's begin with the most obvious advantages of LaTeX over Word: To begin with, it's free. It's well-supported by highly knowledgeble users. It's easily portable cross platforms. It's so advanced in user support at this point, that if you can think about how you want your LaTeX output to look, someone has already solved that problem and made either a macro or an entire package to use to implement it. I use both kinds of fixes, which I can download for free from the Internet. Also, LaTeX can easily be moves into your HTML file to make beautiful math in your webpages, and this is relatively easy to do, once you have it working in LaTeX.
The obvious advantages of Word over LaTeX is that it might be easier to install, though I had no difficulty installing the version of LaTeX that I use on a Windows 10 platform. It's WYSIWYG! Okay, but that is of no particular interest to me at this point. I can more quickly type out a displayed equation in LaTeX than I can construct the equivalent this in a Word document. Furthermore, I have found that copying and pasting sections of math code in LaTeX almost never created problems for me, whereas, I remember often having problems copying and pasting equations in Word, though this was some time ago.
What about this issues of the learning curve being so steep for LaTeX compared to Word? Frankly, I don't see it that way, except with regards to to issue of dealing with compiler errors that won't let the raw TeX file compile to completion. So, let's deal with that now. A raw LaTeX file, like a raw HTML file is a text file that contain markup characters to instruct the viewer application how to display the text. In HTML, a raw file will almost always 'compile', that is, display, in a browser, and that is by design. The browser takes in an HTML file and interprets it as best as it can and then renders an output that it thinks makes sense. It there are errors in it, you're typically going to have to find them on your own.
But not so in LaTeX. If you have errors in your raw LaTeX file, such as failing to close off a environment defined by two parentheses {..} but you only used one of them, {... In this case, almost certainly the LaTeX compiler will call it an error and fail to compile the code, but it will tell you some line number that the error has either occurred on or before. I'll go into debugging your LaTeX files in a different section.
So, back to the learning curve: If all you want to do in either Word or LaTeX is to present a little bit of math and import and diagram/figure once in a while, you can learn how to do that pretty quickly in either one. But any time you wnat to stretch yourself beyond what you already know how to do, you're going to have to put in the time and effort in either program.
Now let's consider the defaults for math type in Word and LaTeX, considered esthetically. They're okay in Word, but even better in LaTeX. But, in my opinion, the LaTeX math type defaults are not perfect. Yet, I can tweak the defaults to get the math in type to be precisely the way I want them to be, but I don't know if I can do that in Word, or would want to attempt it even if I could. Let me give two examples. The LaTeX default for a displayed integral places the integrand just a little too far to the right for my tastes. The fix is both doable and easy to do. I don't know if the fix in Word for such kinds of tweaking is both doable and easy. In LaTeX, one has virtually complete control over how any page will look. One last comment about relative ease of use: In both Word and LaTeX, one can copy and paste an equation or a matrix or a table, and then edit it, but I have found this process to be easier in LaTeX.
Comparing the esthetics of the prose: In regards to document pagination, right justification, and word hyphenation, I'd call it for LaTeX easily. Maybe this is because the main writers of the LaTeX engine were mathematicians. Anyway, even for my essays that contain no math at all, I usually use LaTeX before I convert them to PDF format. The default hyphenation scheme in LaTeX is superior to that in Word, but even LaTeX does at times need some tweaking. But this is easy to do. If LaTeX encounters a word it doesn't hyphenate properly, you can tell it where to break the word by using an inline command, such as for the made up word "Brosheynitz", which is a word I made up in one of my fiction stories. I can tell LaTeX how to hyphenate this word by simply writing in the raw LaTeX file "Bro\-shey\-nitz". This defines discretionary places of hyphenation. If LaTeX decides it needs to break the word "Brosheynitz" somewhere, it will use the scheme I gave it. Furthermore, one can define an entire hyphenation file that has all your predefined hyphenations in it, and make an \include command to import this file.
Now, I must declare one area where I think that Word as better output than default LaTeX, and that is in its letter spacing within words. Now, to be fair to LaTeX, most of its printed words look just fine, but some don't. Words like 'possess' and 'project'. These words appear to me as a little too spread out on the page. To deal with this, I defined a bunch of LaTeX macros, such as
\newcommnd{\possess}{p\kern-.2pt{}ossess}
\newcommnd{\project}{pro\kern-.3pt{}ject}
The effects of these macros is to tighten up the letter spacing to fit my own sensibilities.
So, I create most of my fiction in Word and then export them to PDF for uploading to my website. But most of everything else I publish in PDF is generated in LaTeX, whether it has math in it or not. In the latter case because of LaTeX's superior right justification algorithms for prose.
So, what is my recommendation for the Word vs LaTeX choice? Well, that's complicated. So far, I've only dealt with internal considerations for Word vs LaTeX, meaning: cost, ease of installation, ease of routine use, learning new tricks, esthetics of output. But now we come to the external considerations, such as interoperability with collaborators, institutional requirements (if any) at a college, university, or company, requirements of publishers, etc.
As for myself, I'm not currently submitting papers to journals, but if I did in the future, the journals I most likely would submit to would certainly want the submission in some form of LaTeX, so I'm ready to go. (Publishing houses sometimes require submissions to be in their own 'house' version of LaTeX.)
But let's consider a simple case: That of a high school math or physics teacher, say, who only wants to publish study papers or test papers for his or her class. Should this person use Word or LaTeX? If this teacher is already in his or her 60's then just use whatever they're already using. But if he or she is in their 20's, use LaTeX if possible. LaTeX is free and easy to install (at least on a Windows machine). Also, it has abundant free online assistance. Both Word and LaTeX are easy to learn how to do simple, routine math typesetting and importing of figures/diagrams. If you haven't already learned how to typeset math in MS Word, you're going to have a learning curve to ascend, just as you would for LaTeX.
If you know from the start that you will at some point need to typeset complicated mathematics, use LaTeX. If you are a student, find out what your teachers/professors require of you and also find out what your thesis committee will require of you. It may or may not be LaTeX. If you will eventually want to collaborate with others in publishing technical papers or books, find out if your collaborators use Word, or LaTeX, or something else entirely.
One of the biggest drawbacks for non-techies (in Windows) is how to spellcheck your document. I enter my .tex and .html documents into MS Word to spellcheck them. Why not? I legitimately own Word, so why shouldn't I use it?