jQuery does good jobs when you're dealing with browser compatibility. But we're living in an age that fewer and fewer people use old-school browsers such as IE <= 7. With the growing of DOM APIs in modern browsers (including IE 8), most functions that jQuery provides are built-in natively.
When targeting only modern browsers, it is better to avoid using jQuery's backward-compatible features. Instead, use the native DOM API, which will make your web page run much faster than you might think (native C / C++ implementaion v.s. JavaScript).
If you're making a web page for iOS (e.g. UIWebView), you should use native DOM APIs because mobile Safari is not that old-school web browser; it supports lots of native DOM APIs.
If you're making a Chrome Extension, you should always use native APIs, not only because Chrome has almost the latest DOM APIs available, but this can also avoid performance issue and unnecessary memory occupation (each jQuery-driven extension needs a separate
