(Disclaimer: Not my project, but I've developed several Markdeep-adjacent tools [2][3].)
[1]: https://casual-effects.com/markdeep/
[2]: https://github.com/doersino/markdeep-slides
[3]: https://github.com/doersino/markdeep-diagram-drafting-board
There are some fundamental differences between the two tools. For example, in Markdeep, the user input goes into the <body> element whereas in TeXMe the user input goes into the <textarea> element. The choice of <textarea> element was made in TeXMe to make Markdown rendering more robust. Copy-pasting a valid Markdown code into Markdeep may not always render correctly without further editing. By the way, TeXMe also supports content in <body> as an optional feature.
Further, Markdeep does not care about conforming to the CommonMark spec whereas TeXMe does. If you care about CommonMark spec, TeXMe is a good choice. However, if you need additional features like tables, diagrams, etc., Markdeep is a good choice.
For a detailed comparison of the two tools, please see this thread: https://news.ycombinator.com/item?id=18314175.