In general use Builder inline when creating your widget tree in a build method. This is usually helpful when you need access to a context in your widgets subtree. for example:
Also see this SO question
 @override
 Widget build(BuildContext context) {
   return Scaffold(
       appBar: AppBar(
         title: Text("Home"),
       ),
       body: Builder(builder: (thisLowerContext) {
         return RaisedButton(
             onPressed: () => Scaffold.of(thisLowerContext)
                 .showSnackBar(SnackBar(content: Text("button was clicked"))));
       }));
 }
Use StatefulBuilder when you need access to the setState of that subtree. This will rebuild only the StatefulBuilder with its subtree. 
class _SomeWidgetState extends State<HomeScreen> {
  Data data;
  @override
  Widget build(BuildContext context) {
    return Scaffold(
        appBar: AppBar(
          title: Text("Home"),
        ),
        body: StatefulBuilder(builder: (thisLowerContext, innerSetState) {
          if (data == null) {
            return RaisedButton(
                child: Text("Load data"),
                onPressed: () async {
                  Scaffold.of(thisLowerContext)
                      .showSnackBar(SnackBar(content: Text("Loading data...")));
                  var loadedData = await _loadData();
                  innerSetState(() => data = loadedData);
                });
          } else {
            return RaisedButton(
                child: Text("Reload data"),
                onPressed: () async {
                  Scaffold.of(thisLowerContext).showSnackBar(
                      SnackBar(content: Text("Reloading data...")));
                  var loadedData = await _reloadData();
                  innerSetState(() => data = loadedData);
                });
          }
        }));
  }
}