JPEG and PNG don't work the same way. JPEG is lossy - it removes information from the original image, and PNG is lossless. For distribution, like on a website,

JPEG and PNG don't work the same way. JPEG is lossy - it removes information from the original image, and PNG is lossless. For distribution, like on a website, with JPEG you can compress the image much more than PNG without the users noticing IF the image is photographic. If the JPEG represents a drawing, a screenshot, or contains labels, the lossy compression will be noticeable and PNG is much more appropriate. To keep as master for further modifications and compressions, keeping an image in JPEG format is a bad idea, again because JPEG is lossy. You can't ever encode an image with higher fidelity in JPEG vs PNG but both are useful.