If you’re referring to the DAC portion that does make a difference obviously but that doesn’t have to do with the CD itself or tracking.
The two players have 20 years of development apart. First one was a lower cost Sony, and the latter one is an entry level, yet higher end one (Yamaha CD-S300).
On the tracking stability, first one skips if you knock it lightly, and Yamaha doesn't care if you bump into it accidentally. Also, newer electronics can switch much faster, and in turn, creating a clearer eye pattern for DAC to work on [0].
When you used CRW-F1's audio mode, it elongated the pits and lands, so the digital part had more time to switch properly. This created a clearer eye pattern.
A clearer eye pattern allows DAC to create more cleaner signal since it switches and understands the signal much better and allows it to create a more "correct" (or clearer if you pardon the term) analog signal, esp. on higher frequencies.
Digital data on a Red Book CD is encoded with CIRC error correction, which provides an extra parity byte for every 3 data bytes. In normal operation, the recovery of the digital data is 100%. The DAC receives a stream of 1s and 0s, there is no "clearer eye pattern" for it to "interpret". The data is read or it is not. If it is not, the error is corrected. If it is uncorrectable, for example if there is a particularly large scratch, then - and only then - an attempt will be made to "guess" the signal.
Unless the CD is scratched, a 20$ computer optical drive with digital SPDIF output will be completely indistinguishable to a DAC than a drive costing 100x as much.
The "tracking stability" you mention in the newer model is simply a larger buffer, so that it has time to recover the read.
That said I see no usage for a CD player anymore, really. I can rip a bit-perfect copy, store it in FLAC, and play it pretty much anywhere. The only place I still use CDs sometimes is my car, because it's more convenient than fiddling with my phone sometimes.
OTOH, Listening CDs and vinyls is more of a ritual for me. A good coffee, some good reading material (or nothing), an album I especially like and an hour for myself. That Hi-Fi set also has USB/iPod connectivity over the CD player (and its DAC is a treat for both MP3s and over the iOS streaming) and it has bluetooth connectivity for very lazy times.
So a vintage set with some modern connectivity, and some older formats for enjoying the music for the sake of music.