I’ve always, a few decades that is, used double brackets for internal links, and the other format for external links.
Not sure which software I started this practice, but I’ve turned down some software over the years because they didn’t support the double brackets. But I’ve always found a way to keep using them, and I like the look of them.
[[link]] is wiki syntax and [text](internal relative link) is Markdown syntax.
As you’ve found, Markdown is much more widely compatible. If you set Obsidian to use Markdown syntax by default, you can still type the wiki syntax to get autocomplete suggestions, which will convert to Markdown when completed.
Wiki syntax is simpler, and easier to read and write. It’s appearing in more apps, but will probably always be less compatible because instead of explicitly pointing to a file path, it says to open the file with that name that exists in the vault folder — and not all apps have a concept of a special dedicated folder like that.
I use the default wiki syntax, but when/if I eventually run my website from Obsidian and a static site generator, I’ll use Markdown links by default.