I'm curious about the audio connection capability here, it only works for audio input from my computer and maybe for sending it back from the digital audio out (on the TV) to a home theater system?
Not sure what you're asking here. The DVI port from your computer does not carry audio
With the 40EH5300, that apparently does not matter as you will need to run a separate audio connection to the TV anyway. This gives you audio through the TV's speakers. If you so desire (and your receiver has the proper inputs), you can use the TV's audio out capabilities to have audio go through your receiver's speakers.
With the 40EH6030, you need to run an HDMI to HDMI cable from your PC to the TV in order to get audio from your PC. If you run a DVI to HDMI cable, you will not get sound from your TV at all. You could, however, run the DVI to HDMI cable to your TV and a separate audio cable from your PC to your receiver (again assuming compatible inputs/outputs).
Concerning picture quality, a digital image is a digital image. Both DVI and HDMI are digital ports. There is no real conversion of the digital video signal and there is no degradation. DVI to HDMI will look exactly the same as HDMI to HDMI.