if you already know function and element is part of html i.e. not get added dynamically than its good that you add function inline rather than using extra method call like "addEventListener"
Another thing to note
While onclick works in all browsers, addEventListener does not work in older versions of Internet Explorer, which uses attachEvent instead.
OnClick is a DOM Level 0 property. AddEventListener is part of the DOM Level 2 definition. Read about this : http://www.w3.org/TR/DOM-Level-2-Events/events.html
inline event handlers added as HTML tag attributes, for example:
<a href="gothere.htm" onlick="alert('Bye!')">Click me!</a>
The above techniques are simple but have certain disadvantages: they allow you to have just one event handler per element. In addition, with inline event handlers you get very poor separation of JavaScript code from HTML markup.
document.getElementById("my_id").addEventListener("onclick", my_JS_function, false);
Advatange of this : you can add multiple event handler. also separte html and javascript code
For more detail you can read this : Adding an Event Handler