Personally I'm a big fan of CDs, mainly because they are what I came of age with musically: Got my first CD player for my 16th birthday in early 1985, and summer/fall of that year was when the global production backlog started to ease and albums on CD became truly widely available in the U.S. without the huge time delays compared with LP and cassette pressings that had plagued the CD format in North American up until that time. I had been buying LPs since about 1982 when I was 13, but my mid-teens were when my musical taste really got cemented and at that time it was all CDs for me.
At any rate, I would say it's certainly possible that a new DAC could result in a small but noticeable difference in sound compared to an old CD player. However, I'd say the most likely causes of such a difference would be newer/different analogue output components or power supply/noise improvements.
The digital reconstruction filters will also likely be different, but I am hesitant to attribute any real difference to that, as I've only ever heard filter-related differences in sighted listening comparisons and I suspect they'd disappear if I took a blind test. (I did, however, once see a fascinating comparison online showing how "apodizing" filters favored by Bob Stuart/Meridian could in certain situations actually result in the disappearance of certain transients. It wasn't a "sound quality" thing - it was an A/B comparison where the transient simply wasn't there when the apodizing filter was used.)
@julian_hughes is indeed correct that the earliest Philips DACs were 14 bit units. However, even 14 bits gives a noise floor of just over 84dB without dither and something like 105dB with dither, which is going to be indistinguishable from 16-bit in most home listening situations. Moreover, my understanding is that some (all?) of those early units used two of the 14-bit chips together, in order to achieve 16-bit resolution.
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@qec I would say that since truly excellent outboard DACs are available today for very little money, why not try one and see if you hear a difference? I'm not in favor of high-dollar audiophile "musical chairs" with constant equipment swapping. But this is a hobby after all, and it's meant to be fun - if you can get a great DAC for $150 or less, why not give it a shot?
If nothing else, you'll be prompted to listen to a lot of your CD collection again, with a new level of focus, and that can be fun in and of itself.