The Denon Link III is a digital connection proprietary to Denon, which offers SACD and DVD-A transport which cannot be transmitted over Optical or Coax digital connections.
In addition to the excellent video processing, the beauty of the 3910 is in its analog audio processing. The Burr Brown DACs in the 3910 will be superior to all but the most high end pre/pros and receivers. It also offers excellent processing for distance correction, level matching and bass management but now this feature is offered in most pre/pros and recieivers mid level and up, making it somewhat dated.
When you send digital signal from the 3910 (over Optical, Coax or Denon Link) you will essentially bypass the player's superior audio processing capabilities and be limited to the quality that your pre/pro or receiver can achieve.
EDIT: JcP beat me to the response and he bring up a very good point about digital audio over HDMI. The 3910 can send LPCM over HDMI but it needs to be enabled/ configured in the Audio Setup menu.