I thought there is decent CardDAV support on Android, but I never really checked (I don't use it).

Here is what's coming up with simple search in Google store:
https://play.google.com/store/search?q=carddav&c=apps

Looks like it's not a built in support, but requires some extra applications. On the other hand CardDAV is probably the most cross platform solution, since others are even less common.