Coaxial and Optical SPDIF transmit the following:
-Dolby Digital 2.0 - 5.1 (6.1 Dolby Digital EX Matrix surround sound)
-DTS 2.0 - 7.1 (DTS-ES discrete 6.1/7.1 and Matrix 6.1 surround sound)
-PCM 2.0 (48kHz / 24 bit maximum)
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HDMI has the cability to transmit DSD (direct stream digital) which is what SACD 2.0 - 5.1 is encoded with instead of PCM (pulse code modulation). The catch, both the player and the receiver have to be HDMI 1.2 and ready to handle DSD streams. HDMI also can transmit MLP Lossless 2.0 - 5.1, the format used to encode DVD-Audio discs. This requires that the player and receiver both support HDMI 1.1 and are ready to handle those streams.
Analog connections are specifically put on the player to take full advantage of SACD and DVD-Audio. Given that SACD and DVD-Audio pre-date HDMI it is exceedingly common for SACD/DVD-Audio players to feature 5.1 (6 channel) analog outputs as well as bass management, level trim, and other facilities inside the player to tailor the configuration to your home theater. Because all of the DSD and MLP Lossless decoding occurs inside the player another connection is not required, and unless it's HDMI, it is inferior. In fact, you can only enjoy the secondary tracks on these discs provided they have them.
In the case of Hybrid SACDs there's a secondary 2.0 PCM only track so the disc can be played back in an assortment of standard CD players. In the case of DVD-Audio there will always be a Dolby 2.0 track, and sometimes a DTS 5.1 - 6.1 track. The DTS tracks can sound almost as good as the MLP Lossless ones, but if the material is very involved the bitrate may hit its capacity and data may be lost resulting in loss of dynamics or a mess of sound compared to the MLP Lossless track.