Oi. DVI and HDMI are identical, from the same source (ie computer HDMI/DVI are identical, television DVI/HDMI are identical). HDMI carries audio and video. DVI carries only video.
Now, that said. The computer DVI interface is not eletrically the same as the television DVI interface. To further complicate this, many television monitors will auto-adjust the signal to match the computer interface, when it is sensed. The last wrinkle is there are video cards which will auto-sense and switch to television mode when they detect a television monitor attached.
So, whoever wins is what you get. It could actually change between reboots.
Then again, if neither will convert, you end up with a mess. That mess would also be on the HDMI port, as the video signals are the same, if the device is equipped with a DVI port.
zack, the only thing that could change between DVI and HDMI, in your configuration is who won the battle for which version of the DVI signal to use.