> if I recall correctly JPEG as a format can encode an image with a higher fidelity than PNG, at least in some circumstances

24-bit color PNGs are lossless, to the extent that the input image is encodable in 24 bits of RGB (which is pretty much everything that's not HDR). There's no higher fidelity available for normal input images. If file size limits would force palettized PNGs, it's quite possible for a JPEG at the same file size to have higher fidelity (since it makes a different set of trade-offs, keeping color resolution but giving up spatial resolution instead); but this isn't really a common or particularly valid comparison in the PNG era, was more of an issue when comparing to GIFs.

tl;dr: Nope, PNG is perfect. JPEG can approach perfect, but never get there. Comparison is only interesting with external (e.g. file size) constraints.