HDMI natively supports surround while S/PDIF must use compression for surround modes. Running HDMI through a receiver can add lag and may require the receiver to be on for the monitor to work. A good solution is to use a HDMI splitter. (That requires the receiver to be able to accept the same pixel clock as the monitor, so those running something higher than 1080p would be out of luck with older receivers.) You can also use another output on your GPU (may cause some GPUs to run hotter) or use the onboard HDMI for audio only.
In the end, while HDMI seems to be a great idea on paper (minus the DRM junk, that is) and is certainly very usable, I kind of wished they implemented the audio part as an extended version of S/PDIF so that a passive adapter can split the audio and video signals.