Sounds like the behavior early in the El Capitan release cycle (pre-10.11.2) where the old version of libccid was included in OS X and the patch needed to be run (
https://github.com/Yubico/ifd-yubico). If you haven't updated to 10.11.2, that would be my recommendation. If you are past that, you may want to try and install the patch anyway. Libccid is essentially a whitelist for smart card devices, and the older versions of libccid (which were on OS X until 10.11.2 was released) didn't include the the U2F/CCID combination modes.
Another small (and less invasive) test you can run is to open the YubiKey NEO Manager, disable U2F mode, then see if the available apps are shown, and the yubico-piv-tool / yubioath commands you were running work.