PNG to JPG: find the quality where the size drops and the picture doesn't.
Your PNG is saved as JPG ten times, at quality 10 to 100, by your browser's own encoder. Each result is decoded again and compared with the original, so every bar below is a real file size and every score is a real measurement. Everything happens on your device.
JPG has no alpha channel, so every transparent or half-transparent pixel has to be blended onto a solid colour first. Browsers blend onto black when you draw straight to a JPG, which is why converted logos often appear in a black box. Pick the colour of the page the image will sit on. The file above is re-encoded with it, and the previews show the actual JPG on three pages.
Each image below was drawn in your browser, then saved both as PNG and as JPG at quality 80. Make your call, then see the measured sizes and scores. The verdict comes from the numbers: JPG wins only if it's opaque, at least 40% smaller and scores 38 dB or more.
Eyes notice brightness detail far more than colour detail, so a JPG can store colour at half resolution: one colour sample for every 2 × 2 pixels (4:2:0). In photos you never see it. On thin coloured lines and small red or blue text, the colour smears past the edges. Each JPG made above was opened and its frame header read, so this is what your browser actually wrote:
Your browser writes 4:2:0 below quality 100 and full-resolution colour (4:4:4) from 100 up. Above that point the red edges stay clean, at the cost of a bigger file.
If the goal is just a smaller file, a modern format may beat JPG outright, and keep the transparency.