Hi Richard!
It depends whether or not you are concerned about file size or image quality.
1) PNG is lossless format when compressed; you don't lose image quality when it is compressed. They also can have transparency effect (most often used in the background), whereas JPEG will only show white for transparent effects.
PNG offers higher picture quality, but at the cost of bigger file size.
2) JPEG is a lossy compressed file format. This makes it useful for storing photographs at a smaller size than a BMP. JPEG is a common choice for use on the Web because it is compressed and has smaller file size.
So in short, JPEGs are for photographs and realistic images. PNGs are for line art, text-heavy images, and images with few colors such as icons.
Usually, people like to upload graphic images for their avatars such as cartoons characters. In this case, PNG is the better choice. As for cover, it's better to use JPEG because due to its size and people usually like to upload realistic pictures.
Of course, this is not a rule that you must follow. If you want convenience, JPEG is good for both because of its smaller size. You'd less likely run into storage issues.
That or just allow the user to upload whichever file format they want to use
I hope this helps