I use DACs from that series pretty often and they are just fine. However, the AD5624R is 12-bit, not 16 as you said you need!
Yes, the AD5664R is the 16-bit one.
But since the OP compared it with the DAC8562, which IIRC is 2-channel DAC (and the DAC8564 the 4-channel version?), maybe they have the numbers confused, and meant to pick a 2-channel, 16-bit DAC in this AD56 series? In this case, the 2-channel, 16-bit one would be the AD5689R, for instance.