No, they're definitely not equivalent in the general case. The :even and :odd selectors apply to the even/odd elements in the jQuery object. Depending on what has come earlier in the selector, those elements may not even be related in any way.
In contrast, :nth-child(even) selects the even children of the element(s) in the jQuery object. The example in the documentation does a pretty good job of demonstrating this: http://docs.jquery.com/Selectors/nthChild
