What are you streaming?
I stream Tidal and a few internet radio stations and never got an acceptable answer from TEAC on the ZCD being compatible for Tidal.
In fact the answer was a "no we do not plan to support that" but it was a while ago.
For that reason, if it matters, I would go with the ZDSD and stream from your existing setup.

Then the ZCD may be fine.
However, I remember some comment from Steve back when I was considering this same choice about the ZDSD DAC being the best of the two. I'll look for the thread.

PS: This is it.....
https://www.decware.com/cgi-bin/yabb22/YaBB.pl?num=1438614503/9#9

Between the two I find the ZDSD has a higher potential for density and usually delivers it when you get the output level set anywhere near -20dB.

That said, I use both the ZCD240 and the ZDSD. I simply use the ZCD240 as a transport which is connected to the digital input of the ZDSD. This way I can use the ZDSD as the DAC for ZCD and I do. However, having the ZCD240 I have on many occasions listened to it by itself, and I have to say it has a slightly lighter on it's feet delicacy and transparency that I find so appealing that I could easily live with it as my only digital source if I had to. Many nights both were there stacked on top of each other but the drive to hook up the ZDSD just wasn't there because I was enjoying the music almost equally well but from a slightly different perspective.  

If you go with the ZDSD, get yourself a stock Tascam CD240 as you wouldn't be taking advantage of the Decware mod, other than the power cord which we replaced with our own shielded cord to lower the noise floor. Granted it's not our silver teflon cord, but that cord is unshielded and in the world of network players, noise on the power cord will effect your perception of liquidity in the music. If you go with the ZCD240 know you are getting almost equal sound quality, less dense, but more air. And let me say that with the Decware output stage less dense in this context means that the player is only 804% more dense than a typical 2 volt output stage vs., the ZDSD's 940% density increase. Pretty much a mute point relative to the norm.

You might also find it a viable option to purchase a ZBIT and hook it to the balanced outputs of either machine.  The result is 95% as good and the same parts are used in all.  The advantage of this would be the fact that the ZBIT will never wear out or fail because it is a passive device with no capacitors or circuit boards.  It can be used for hundreds of years with all your future balanced sources or preamps.

Steve