I just created a CMYK/8 Fogra 39 document and placed a Fogra 39 photo, created text, etc.
I see your concern. When viewed in Finder or Graphic Converter (Mac), the PDFX1a document does look darker than the Press Ready exported PDF.
So, I opened the PDFX1a exported document in Affinity and compared it to the original document (in its original AF file format). The two files look identical and the color numbers match between the two, so I think the exported PDFX1a file is fine.
I believe the file viewer (in my case, Finder or Graphic Converter) is displaying the "untagged" PDFX1a file using a default ICC profile, which results in a color/density shift on the monitor. When you look at the Resource Manager in the re-opened PDFX1a file, you will see that the placed image is shown as CMYK, but WITHOUT the Fogra 39 profile, (the profile was stripped on export to PDFX1a), since PDFX1a bases color interpretation on the Output Intent and the image tag is no longer relevant. That's the way PDFX1a was designed for Press. Most of the basic PDF viewers don't know to use the Output Intent for color management and display, so they use some generic profile (usually sRGB or US Web Coated SWOP v2). You need a Full featured PDF Analysis tool for Press (Acrobat Pro, PDF Toolbox, etc). One of those tools, (or re-opening the PDFX1a file in Affinity) displays the file correctly, because they are designed to support Press workflows. I am pretty sure that's what you are seeing.
The other PDF Export modes (for Print, Press Ready, etc) are fully color managed workflows and as such, embed ICC profiles into the exported PDF. Most decent PDF viewers will see and properly apply those ICC profiles and color manage the files when displayed on your monitor.
I haven't been doing any Press work for a while, so perhaps one of the more actively involved Press folks can weigh in and confirm what's happening. I think this is the answer to why your PDF files display differently.