No, in general there is no difference in print quality between any PDF versions. I can think of only two exceptions:

· If you're embedding ICC color profiles, you need to be using at least PDF version 1.3, which came out in 01999.

· If you're embedding lossily-compressed raster graphics like JPEGs, while you can always improve the print quality further by switching to losslessly-compressed graphics like PNGs, you may be able to get better quality at a given filesize by using better lossy compression algorithms like JPEG-2000 or (for bilevel images) JBIG2. JPEG-2000 support was added in PDF 1.5 and is excluded from, I think, PDF/A. JBIG2 support was added in PDF 1.4, and also includes a lossless format.

I don't know of any features in 2.0 that would improve print quality over 1.5 in any way.

It’s probably worth spending a few minutes looking into PDF/A, which is a subset of PDF designed for archival. While it might not be a perfect fit for your needs (though it almost certainly is), being ISO standardised it might be a good source of documentation.

https://en.m.wikipedia.org/wiki/PDF/A