Around 1997, people making pop, rock, rap, and just about all highly commercial recordings, realized that they could crank the volume of their digital recordings during the mastering process. They could do so because digital limiters and compressors made it very easy to do without obviously audible clipping. As a rule of thumb, people think louder music sounds better. So if you were listening to some CD from 1996, and then switched to something from the following year, it would sound louder. Superficially, people found that appealing. Artists wanted their CD to sound louder than other artists'. It prompted a constantly growing effort to further compress recordings during mastering, to get them louder than recordings made previously. The limiters used during mastering kept getting better over time too. Unfortunately, all of this heavily compromised the sound quality. Smashing loud peaks drastically reduces dynamics. Subjectively for me, that destroys the illusion of depth. I would also describe the sonic effect as a flattening.
Vinyl can't be mastered like that. Smashed peaks will cause the needle to jump off the record. So this asinine competition for loudness can't happen there. It has to be mastered differently.
Try this, take two CDs of the same genre. Pick one from the early 90s. Pick another from some time in the past ten years. I'd say there's a 95% chance the newer CD will sound very noticeably louder. Better yet, find two masterings of the same album, where one is from the 80s or early nineties, the other is from the past decade. Again, I almost guarantee the newer master will sound much louder. But sadly, the old will have a much better sense of depth to it. And this is despite the fact that analogue to digital conversion has improved drastically since the 80s.
So, when comparing different formats of any kind, always be mindful that they were most likely mastered differently. And unfortunately, that makes true comparisons almost impossible.
Most likely, "Popular Songs" was recorded digitally. If so, there can't be any added fidelity by converting it to analogue.
So, enjoy those records. I have no doubt that they do sound better. It's just not because there's an inherent advantage over digital.