I never used Flutter for Desktop, but, what I think is different between the too is the same difference that Flutter and Android Native has, that for any specific OS related that does not have any plugin yet, you will need to create a plugin (specially for Desktop version that is pretty new). This is not the case for Compose for Desktop, because it's runs in the JVM, so, everything that exists for the JVM you can use with Compose, there is not need for plugins.