I usually do not write this, because people that spend a lot of money on such gear may feel insulted.
I'm quite sure there are quite coarse working, cheap DAC chips, without daubt. If we keep these uncapable models out of the comparison, we will have a lot of perfectly fine basic chips, which are the core of any DAC, may it be inside a CD player, DVD, streamer or a separate unit.
Where the "sound", if you can find a specific one, comes from and where the designer can tune it a little, is the output stage.
Cheap CD player with audible worse sound, in most cases have very simple power supply's. If you don't drive an output stage with a clean power, it will have a much harder time delivering a clean output. From my experience, this is a fact.
An external DAC has the advantage of not needing to drive power consuming electric devices, like a motor, laser etc. This puts a much lower load on its supply voltages. I have some CD player that clearly profit from an external DAC, even as the DAC chip inside the drive is of theoretically "better" quality, more expensive or from a much more prestigious manufacturer than the one in the external one.
There are lists with the DAC chips build into any CD player or other D/A converting piece of gear. If you find a separate and integrated unit with identical DAC chips, you can check this out on your own. If it was the DAC model dictating sound quality, both should sound identical. IMO even if the analog output stage is using the same IC, like a NE5532 which is quite good, in most cases you will hear differences.
If you are objective and match levels, your findings may not be what you expect or want to hear. There are very cheap DAC's in the 30$ range that match or even sound better than quite expensive CD drives. Maybe high integration is better than old school, large PCB areas with many parts. Just an idea.
Because of the various components that are needed to build a working DAC, from it's input to it's output, I don't think there will be a final answer to the thread's question. You can only answer it for your self. By the way, a 12$ multimeter in the AC range and a 400Hz or the like test CD, burned from some
free file, is the base you need for a serious home test. Without matched levels you will fool yourself.
In all honesty, I don't expect any new DAC, as expensive as it may be, to sound better than the existing, good ones. The differences are just not there. I fear there is just as much honesty when improvements are presented, as there are with cables. You simply can not get better than 100% perfect, even as most of the audio industry is living on this well-fed illusion. If you want to really improve your audio chain, today 99.99% are in the speakers.
And don't use compressed audio that is not loss less, whatever someone tells you. Missing data are missing.
PS I may add one observation. Valve output stages, may they be inside a CD player or DAC, can seriously change the sound. Sometimes very nice I must admit. If you like it or not, is your personal decission. This is not a sign of the valve concept's superiority, but just a side effect of an outdated electronic part, changing the original signal. I know, there are many fanatics working in this area, but simply because you need more, heavier and more complicated, expensive parts, something must not be automatically better than a state of the art, 5 Volt driven, integrated 40 Gram solution.