Wikipedia has an excellent article on JPG compression
JPEG - Wikipedia (lossless editing)
But I think the sensible answer is that using the default setting will protect your sanity, and pixel peeping in general will surely lead to madness. Of course context is important here. We have a colour obsessed regular poster who works recording museum quality art, so it is obviously crucial that he takes every possible step to maintain accuracy and image quality, but I doubt he does so using JPG. It has also clearly cost him his sanity, as he is as mad as a box of frogs.
If you are interested in the practical aspects of your question, find a high resolution busy image (the more complex the image, the harder JPG compression has to work.
Save the image once using Baseline, and again using Progressive with quality maxed out to 12.
Open the two saved copies, and name the layers so you know how they were saved.
Drag each layer to the original, and align them. (Select the layers and go Edit > Auto Align layers and choose reposition.
Now set the blend modes of the two higher layers to Difference
If you duplicate the background (unsaved) layer and set it to Difference, you will see perfect black for each pixel. That will not be the case with your two saved layers, but the difference will be very subtle. I suspect you will not be able to say one was better than the other though.
Personally, I feel content is more important that absolute quality.
I hope this helps