The use cases are different for me, personally. There are some minor (on the surface), but major (depending on how you use the software) differences between them out of the box:
- Logseq is focused on daily journal pages and pages with lots of linkages, the idea being it keeps you on focused on tasks without feeling like you are spending too much time tinkering, organizing, or like you have to build out a perfect system right away. I like it for work because it lets me work "in my notes" rather than needing to work "on my notes" if that makes sense. I'm aware of similar Obsidian setups, but having it work out of the box in Logseq means many of the other design choices in the program are made with this workflow in mind.
- Every note is structured as a tree with hierarchical items (blocks) nested within one another. This means every block has a reference, so it's easy to create and maintain links to different pages. Obsidian does support block references out of the box, but you have to insert them for every line you want to reference because it isn't set up to enforce a tree structure by default.
- Tags and note links are interchangeable. I would actually say this is the main point against vanilla Logseq compared to Obsidian. There are plugins you can use to give tags different behavior to links though.
- The community seems smaller and there aren't as many plugins. Many plugins don't seem to be well supported or maintained, but they are usually pretty focused on solving one particular problem.
I use Logseq for work where being able to reference blocks is more useful (especially for task management), and Obsidian for personal projects where I feel a more free form PKM with customization options is nicer.
I use both for different use cases, so I've never used the same directory for an Obsidian vault and Logseq graph. Pretty sure they would both be able to read and write the markdown files, but would features like Logseq block references and queries work in Obsidian? How would Logseq treat Obsidian bases?