Logseq and Obsidian are only similar on the first look, but very different usage wise. Both are very open with a plugin system, and you can modify them to turn them into one eachother.

So, if you want only FOSS, then Logseq is the only choices you have.

But Obsidian is, even though it’s proprietary, very sane. Open plug-in system, active community, great devs who don’t have much against FOSS, and more.

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Obsidian

• More similar to a classic note taking app, like OneNote, but with a lot of features. Hierarchical structure, and more of an “essay” style, where you store a lot of text in one page.
• Page linking is only done when you think it makes sense
• Has been a bit longer around than Logseq, feels more polished
• Great sync and mobile app, which support plugins from what I’ve heard

Logseq

• Non-linear outliner. Every page is on the same level, but within a text passage, the indentation matters (parent-child-relationship)
• You create a LOT of more pages. Most of my pages are empty. They are mainly there for linking topics. I rarely create pages manually.
• The journal is where you write most stuff. You then link each block to a page.
• Logseq a bit “special”. May not be for everyone. I for example am a bit of a disorganised thinker, who mentally links a lot of knowledge and throws concepts around all the time. Logseq is my second nature, because it’s more flexible. My GF on the other hand is more structured, and prefers something like Apple Notes, or, if she would care about note taking, something like Obsidian.
• The mobile app isn’t great. It’s fine when I’m not at home, but the desktop version is the “proper” one, and mobile/ iPad a second class citizen.
• Sync is only experimental for now. It will soon be officially supported (hopefully) and self hostable, but it worked fine for me.