Serializable is simpler to implement (The minimum is to just "implements Serializable) and simpler to extend (e.g. it manages inheritance)
Externalizable gives you most control, but you have to do more yourself.
If you are starting out, just use Serializable. It turns out to be inadequate then you can convert the classes which need Externalizable to be be those.
Note: You don't have to just use one or the other.