I2S Input - Is It Better?

It's a regular HDMI.  Some use an RJ45 connection. 

Generally the i2s output will yield a more accurate, cleaner sound. Tighter imaging and placement within the soundstage. Bass tends to get more defined.

This can come at the expense of sounding lean. 

Unfortunately there aren't many audiophile type HDMI cables as they are mainly for video

It depends, it looks like an HDMI cable and some companies use the same pin out but leave some disconnected. Some use their own pin out so you need to look in you manual it should show you. If they're both the same brand they will probably work together if not you might have to open them up and set jumpers. 

Unfortunately there aren't many audiophile type HDMI cables as they are mainly for video

Why, sure there is 
The following Audiophile Cable companies make HDMI cables
Acoustic Zen
Analysis Plus
Audioquest
Chord 
Crystal
Dh Labs
Furutech
Harmonic Technologies
Kinber Kable
Purist Audio Design
Straightwire
Van Den Hul
VooDoo Cable
Wireworld Cable Technology
Black Cat Cables
Nordost
Morrow Audio

and that is not all

As I understand it, one must make sure that with HDMI I2S connections the pin orientation on both devices to be connected are the same. 

Actually it is hard to tell if I2S is actually superior for there are very few devices for sale that go directly into an I2S connection--that is other than those that convert either spdif or USB to I2S. A quality DAC should already have quality spdif and USB inputs with the conversion to I2S done internally.

Some DAC I2S connections use ethernet connectors; some use HDMI cables. Mine uses both. The ethernet cables are fairly easy for an amateur to alter to meet I2S needs. Some units that feed into I2S have a bunch of dip switches so that no specially made up HDMI cable is necessary.

But I2S, which is how a DAC communicates internally, has never been much use to audiophiles as there are very few units that feed directly into it--the reason being that there are so few DACs with an I2S input. There are some bridges feeding I2S that are relatively expensive and one reasonably priced that is not a terribly high performer. So all the R&D goes into those feeding USB or spdif.

So theoretically yes, but in practice no.