The Sony BDP-S380 doesn't have support for DVD-Audio or SACD discs, HDMI or not. You'd need a player that can handle both those formats if you wanted to listen to them. Players to look at would be the Panasonic DMP-BDT500, Oppo BDP-93 and 95, Cambridge Audio 751BD, Yamaha A1010, and probably some others. Even if you're using HDMI, the player still needs to decode DVD-A (which is in MLP format on the disc) to PCM for transport over HDMI, and be able to convert DSD on an SACD to PCM, or send it as native DSD, which most players can't do.
With a receiver, you might want to track what players and receivers can natively do DSD over HDMI, if you are going to listen to a lot of SACDs. Some people prefer it to converting it to PCM (I'm not taking a position on this, as I haven't done an A-B comparison), but if you are going to use the room correction or bass management in the player or receiver, it almost certainly needs to be converted to PCM to do so.
Edited by Smackrabbit - 7/25/12 at 8:58pm