I agree with George that the 24/96 is the best, but unless you are upsampling, the 24/96 dacs are only reading 16/44...
The key is to add an upsampler (i.e. I use DCS Purcell), which will upsample 16/44 to 24/96 (or even higher, like 24/192 if you have a dac that can read it- i.e. DCS Elgar). Once upsampler is in the mix, THEN the 24/96 dacs WILL read the upsampled version, providing the superior sound.
And back to the original question, yes, HDCD and 24/96 can be mutually exclusive. The HDCD is a chip (in absolute terms, it really just provides a filtering function)- I believe the HDCD chip in my Sim Audio Eclipse CD player is a Pacific Microsonics PMD-100. Whether or not your dacs can read 24/96 is a separate issue. Hope this helps!