I do a mix -- paper is for thinking, digital is for long-term saving.
I'll use paper (nice paper and a fountain pen, ideally) for a quick brain-dump, mind-mapping, planning out my week, figuring out the shape of a solution. There's something about working on paper that spatially makes more sense to me. I keep it all in a single notebook *usually A5 grid or dots like Leuchtterm 1917 or Rhodia webbie) so that I don't have loose pieces of paper. If I'm working or traveling, that notebook is in my bag.
Things that I need to remember land in Obsidian in cross-linked notes, usually tied together with a daily note. Some paper notes do land in Obsidian - that can be a photo/scan, but more likely a cleaned up, summarized version of my thoughts.