My understanding is that saving as JPEG (more accurately, JFIF) with "100%" quality does not mean lossless compression. It means (approximately speaking) 100% of the possible fidelity available using the lossy JPEG compression. Or, to put it another way, "the least amount of loss possible". You will still lose image quality. (You may also quite possibly end up with a larger image than you would have using PNG.)
That said, there is apparently a (non-JFIF) JPEG standard for lossless compression, but AIUI it uses a different file format and is not commonly used or implemented.