public class Foo : Object {
    public string prop { construct; get; }
}

It is meant for interospectable API using GObject Introspection. This is the recommended way for declaring classes.

public class Foo {
    public string prop { construct; get; }
}

Pure-Vala and lightweight class. This is useful if you need a compromise between efficiency of a struct and the feature of a full blown GObject class.

[Compact]
public class Foo {
    public string prop;
}

It is mainly used for writing bindings with specific memory management.