The answer is YES!
If you have opened up a CDP or a DVD-Rom drive and look at how the disc spins, you'll noticed there's a lot of wobbling. This creates a lot of reading errors and need to be corrected. The error correction for the CD is often "acceptable" and not true original data. In the peak of Rom drives era, there are many websites doing tests and looking at errors and correctable errors via scope, how well each brand and model does. The least read errors with best correction algorithm wins.
The same goes for cd/SACD players. Many brands have their own way of having a very high quality read from the disc to start, eg. using glass lens on the laser pickup, having 3 laser to track and averaging out the errors, using a bigger heavier clamp, reducing spin speed, adding light noise to the red laser, using green laser as pickup, etc etc. All these are to aim at minimising read errors so less correction is needed.
After the read, next up is the data processing before sending to digital out. This part makes another difference in sound quality.
I've not heard the Project or Jay's. What I can sum up from my experience is: Basic entry good quality transport is the Audiolab 6000CDT, next upgrade would be the Cyrus XT signature transport, higher end goes to YBA transport with a blue laser, and the ultimate transport goes to Esoteric with their VRDS mechanism. The first 3 only do red-book CD.
There are many other players and transports I heard like the CEC, Marantz, Pioneer, Oppo 205, Cambridge Audio, Mark Levinson, Roksan, but my vote goes to those 4 only.
Have fun shopping for a new transport. Let us know what you finally decide to go with.