JPEGs are fine for pictures of text. You need to set a high enough quality setting and/or resolution, however.

PNGs, in turn, suck balls for pictures of text. You know, the ones you take with a camera. Sure, there's no distortion, but since they'll utterly fail at compressing the analog noise you'll find in the white background of the page, your file size will be ridiculously huge.

PNGs are great for illustrations, diagrams, and images of text with very little analog noise. If not generated on the computer, then at least cleaned up, levels balanced, noise removed by altering curves, etc. It's usually okay for things like webcomics where the author has taken quite some effort to remove this noise, resulting in a nice black-and-white image with long horizontal runs of black or white pixels that the PNG compression algorithm handles well.

JPEGs are great for pictures taken with a camera; their compression algorithm is designed to efficiently deal with the analog noise found in such pictures without rendering the image unintelligible. You'll note that the OP's image was quite readable, and the noise hard to notice until you zoomed in. You'll also notice it was 50KB. The PNG screenshot you saved was 84KB, and it was of a smaller region of the overall image (the zoom-in using nearest neighbor won't affect PNG file size much thanks to its zlib encoding)*.

So, in short, this is not a case where PNG would work better. If you want to get rid of that noise, but still have a decent file size, there are three options:

1. Save as PNG. 50KB image becomes several MB.
2. Crop the image, to just the black-and-white page, then adjust histogram curves and save as PNG. File size increases significantly, but probably remains reasonable.
3. Increase JPEG quality. File size increases significantly, but probably remains reasonable.

I, personally, would recommend 3.

* - Note that recompressing JPEG to PNG will usually result in file size increases. However, the point here is that converting a very small region of the image to PNG results in a file size larger than the original file. Also note that most digital cameras output JPEG format, so you will always end up recompressing JPEG artifacts, unless you go via raw output format (which most people don't know how to do), or spend the time cleaning up artifacts (as well as the other analog artifacts while you're at it; a lot of work, and again, most people don't know how).