I dont know any Ethan's that are shortened, but that doesnt mean they are not. Ethan was always going to be the the name for our son due in October untill we both just decided we no longer wanted it. We still love the name though!!
I like both, but Ethan would be my favourite, but not sure about a shortening of it, as if I had had it I wouldn't want it shortened (out of my 3 children we only have 1 name that can be shortened and we do not shorten it at all).
Ethan. Or Nathaniel. (But I am currently trying to evict a piss-taking lodger called Nathan so I'm very biased!)
But I would have said that anyway, honest! My good friend had an Ethan, it's a lovely, beautiful name. Nathan sounds like a teenager or adult to me. It's a much harder sounding name IMO and nothing special really. (Sorry to any Nathans!) I like Nate but as others have said what about Nathaniel if you're really keen on Nate?