I've used both, and I prefer TeXmacs. Despite what the name might apply, TeXmacs is not built on top of TeX. This is a good thing. It's much less bloated (60 MB vs several GB), and compilations seem much faster. Highly extensible/programmable with GNU Guile (hoping they'll transition to Guile 3 train soon) + plugins. UI is better than 95% of FOSS apps.

LyX requires a LaTeX (or LuaTeX/XeTeX) installation, and comes with its lot of pros and cons. Access to massive universe of *TeX packages. LyX seems more widely used.

> Despite what the name might apply, TeXmacs is not built on top of TeX. This is a good thing. It's much less bloated (60 MB vs several GB), and compilations seem much faster.

TeX is not several GB. It was designed for systems running under intense resource constraints, and it is tiny.

Most widely used TeX installations (TeXLive is the big one) bundle lots of the most popularly used packages by default, but that's an option, and they can be installed on demand as needed. Even granting the reasonable point that modern TeX is functionally useless without packages (and other essential accouterments such as PDFTeX rather than Knuth's original code), I stripped down TeXLive to the packages I actually need (which is an easy choice in the installer, not some arcane hack), and it's about 300 MB.

TeXmacs is its own thing inspired by TeX. LyX is a WYSIWYG editor for LaTeX (which is a thing on top of TeX).

The LyX folks would say it's a WYSIWYM (what you see is what you mean). Great tool. I wrote my dissertation and several papers on it, and it was a huge time saver, and a great way to focus on the content, not the form.

TeXmacs is not built on top of TeX. It is closer to a Lisp.

Yeah that's some pretty terrible naming. Why would you name something that is not based on TeX TeXmacs. Next you're going to tell me it isn't a Mac app.

It isn't anything to do with Emacs either :-)