The documentation is always a good place to start, for instance the stuff you find in the ui object for draggable is available here: http://jqueryui.com/demos/draggable/. The event object is always the original event that is fired, while the ui object contains information added by jQuery UI.
If you want you can also do your own digging. Using console.log on Firefox with the Firebug and Firequery add-ons, you can look at the insides of both objects. For instance, with this code:
$('#test').draggable({
start: function(event, ui){
console.log(event);
console.log(ui);
}
});
The ui object looks like:
