HDMI is different than optical digital or coax digital.
Both optical and coax digital use the s/pdif protocol and perform the same. In some rare cases, coax digital can be slightly more susceptible to electromagnetic interference (because it is electrical instead of optical) but in practice there is no difference. On the other hand, coax cables and connectors are more robust than optical cables which use the fragile toslink connectors. Use either one.
S/PDIF cannot carry high bandwidth multi-channel audio so cannot be used for things like SACD, DVD-A, or multi-channel uncompressed PCM (which is the underlying format of the newer lossless formats like Dolby TrueHD.
HDMI can carry high bandwidth multi-channel audio as well as video and control signals at the same and is the current industry standard.