Sarmad,
The AUDIO16 card's link mentions the C6713 DSK several times and claims to have example software for that board. That certainly tells me that the boards are compatible.
Interrupts are not the same as data channels, so your question does not really make sense. It is good that you clarified it to be accessing data from 16 audio channels. The title line and some of the wording causes us to give you broader answers than what you are looking for.
As I said, since the EducationalDSP website says it works with the C6713 DSK, there is no reason to doubt that. They can help you more with understanding how their board works with the C6713 in terms of getting the data in and out. But obviously they have a way to do that, right?
The PCM3003 page does not mention the C6713 DSK anywhere. Why do you want to use it if you have the other one? Is there a reason you need to work with the PCM3003 in this case? You may want to contact D.Sign.t for more information since this is their board.
Regards,
RandyP