Are you trying to add HDMI out as part of a multi-monitor setup? On most cards one of the DVI ports and the HDMI port share electronics so only one can be used as once, so doubly check your card's documents to see if you need to just rearrange the connections. For instancem if I remember rightly, all standard EyeFinity cards are unable to output to the HDMI and single-link-DVI ports at the same time (but you can use the HDMI port at the same time as the dual-link DVI port and any DisplayPort connectors you have).
As you have it working via DVI, unless you need sound to be played through the TV too I'd stick with that (the only practical difference other than the connector between DVI and HDMI, unless you are playing DRMed content, is that HDMI carries audio signals as well as video.