There are actually quite a few Python-in-the-browser implementations, not just those two! A couple of years ago a colleague of mine wrote up a comparison, including Brython and Pyodide:
(We chose one of the Python-to-JS compilers, https://skulpt.org, for the Anvil web-app platform, because it's much lighter weight than this. It's a couple of hundred kb on the wire, and you can call to the server for any heavy lifting.)
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There are actually quite a few Python-in-the-browser implementations, not just those two! A couple of years ago a colleague of mine wrote up a comparison, including Brython and Pyodide:
https://anvil.works/blog/python-in-the-browser-talk
(We chose one of the Python-to-JS compilers, https://skulpt.org, for the Anvil web-app platform, because it's much lighter weight than this. It's a couple of hundred kb on the wire, and you can call to the server for any heavy lifting.)
And before all of those, 20 years ago, ActiveState had a Python ActiveX extension (in addition to Perl and TCL).
Just the word "ActiveX" brings about nightmares.
One downside with python-to-js compilers is losing easiness and speed to debug issues, which is one of the strongest points for using Python.
It also requires a server somewhere for dynamic input (i.e. Browser based notebooks).