The other thing is onboard/built-in HDMI can support high resolution audio, whereas DVI-Hdmi is audio limited to 5.1 DD/DTS/2chLPCM as maximums.
Going forward some features will only be on HDMI, like deep colour and such are only supported on HDMI. DVI is 8 & 10 bit colour, deep colour includes 12bit and the option for more.
Eas way to compare is intergrated HDMI could do 1.3 and higher, DVI-HDMI is limited in a similar fashio to what HDMI 1.2 is.
Short term not much difference between the two for video.