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Pro Alpha channel
BPG has an alpha channel, which adds transparency to BPG images if needed.
Pro More bits per color channel
BPG is able to render more bits per color channel compared to JPEG. 14 bits vs just 8 bits.
Pro Same image quality, half the size
BPG is able to produce the same image quality as JPEG but at half the size. This is simply because is uses a newer codec, x265 which is the open-source implementation of HEVC/H.265.
Pro Open source
BPG is an open source implementation which only took a few months to be created. It is not created by some international standardization body (like ITU or ISO), which take several years to create and update standards.
Since it's open source, changes can be proposed at any time, and if they benefit the project, they are merged into the main branch. This ensures that the standard is always up to date and that fixes can come quickly.
Con No native support in browsers