Now that you mention it the 360 would have made the most sense to ship with HDMI since the original Xbox was the first console to launch with Ethernet access built-in.
HDMI combined with a Blu-ray player, instead of a separate HD-DVD, could have given it the edge over the PS3. Although Blu-ray is/was a Sony technology they ended up having to do it anyways in the Xbox One ¯\_(ツ)_/¯
Now that you mention it the 360 would have made the most sense to ship with HDMI since the original Xbox was the first console to launch with Ethernet access built-in.
HDMI combined with a Blu-ray player, instead of a separate HD-DVD, could have given it the edge over the PS3. Although Blu-ray is/was a Sony technology they ended up having to do it anyways in the Xbox One ¯\_(ツ)_/¯