It reportedly causes problems if you edit the same file in two different places at the same time, it will generate a conflict when saving since the files won't match, doesn't affect me in my workflow (if I have access to my desktop I won't use it on my phone) but YMMV

Obsidian creates a hidden directory in your “vault,” which contains plugin files, plus metadata about your settings, currently opened files, etc. If those settings don’t work equally well on both systems, that would be a hassle. Maybe try copying all the files from inside the directory (so that you don’t grab that hidden dir when you do) instead of grabbing the whole directory.

You might also want to look at the git-obsidian plugin. It takes a little setup, but seems to work well once it’s going.