The first method is to prefer. It uses the advanced event registration model[s], which means you can attach multiple handlers to the same element. You can easily access the event object, and the handler can live in any function's scope. Also, it is dynamic, i.e it can be invoked at any time and is especially well-suited for dynamically generated elements. Whether you use jQuery, an other library or the native methods directly does not really matter.
The second method, using inline attributes, needs a lot of global functions (which leads to namespace pollution) and mixes the content/structure (HTML) with the behavior (JavaScript). Do not use that.
Your question about performance or standards can't be easily answered. The two methods are just completely different, and do different things. The first one is mightier, while the second one is despised (considered bad style).