HDMI vs. DVI
Here are a few other facts beside the audio being included with HDMI.
From Wikipedia
HDMI is backward compatible with single-link Digital Visual Interface digital video (DVI-D or DVI-I, but not DVI-A). No signal conversion is required when an adapter or asymmetric cable is used, so there is no loss of video quality.
This means that HDMI is not the exact same as DVI Dual link whose bandwidth "is limited only by the bandwidth limits of the copper the DVI cable is constructed of and by the DVI signal's source." Also, there are several specification types and versions to HDMI that limit it's speeds.
With those two combinational factors there's a possibility that a HDMI cable and/or port will not produce the same quality as the DVI and vice versa. For example, with my home PC I ran into an issue with my HDMI cable connected monitor only running at 60Hz vs the 120Hz that I got from the DVI-DL. This can cause issues with 3D enabled content.
Note: There ARE HDMI Cables that can handle 3D content, but not all.
Here are some other sources to look at and a summary of their findings:
The Introduction of the Adapter
Whenever you introduce any type of adapter, you are limited by the specifications of the lowest operating medium. For example, a VGA to DVI adapter is limited by the specifications of VGA. In your case (HDMI to DVI), the limitations are dependent on the individual devices being used. If the receiving monitor is a single link DVI then there is probably no difference in quality. However, if the receiving monitor is a dual link DVI, there may exist a reduction in quality.