If you're not using it for interlacing and transparency, the only real upside would be the compressed file size.
However, you may want to look into using the PNG format. You can find an overview of the three file types here (Surrey University)
Over the past 5 years, PNG has been phased in to the web image standards, developers and designers always knew it handled compression better, but it wasn't fully supported by all browsers - causing it to be overlooked until said browsers were upgraded.
Nowadays, PNG is pretty much the most commonly used file format for images on modern websites.