There are some benefits..
JDownloader is useful to handle batches of downloads, such as when a set of MP3s is put online. I've had problems with FireFox truncating MP3s when I download a bunch at once. JDownloader has sophisticated multiple-download functionality that browsers don't have.
JDownloader will automatically extract many archives, which saves time. You can also set an archive's password in advance, so you don't have to remember it later.
JDownloader used to be useful for batching downloads to run overnight. Since most download sites now require you to type a CAPTCHA with every download, this is less useful now than it once was. I used to batch up a whole night's worth of downloads, and even with hours of waiting time between downloads, JDownloader kept plugging away.
If you prefer to keep a low profile online, and use NoScript/AdBlock/Ghostery/etc a program like JDownloader is useful. You would have to enable Google's web scripts to use ReCAPTCHA in your web browser. If you use JDownloader, it handles that for you, plus the scripts can't track anything else you do in your browser.