I used to think it was the same as the original too. But after listening to both tracks over & over one after the other it became clear that the Alt.mix has all the weird sound effects pushed to the front of the mix ie:the creaking of the rocking chair at the beginning and the pull on the cigarette. The crazed voices at the end are much more pronounced as well. It's great stuff. A really interesting mix of one of his best songs.
Joe the Lion though has no discernable difference that I can tell.
And Look Back in Anger '88 just cannot go on Tin Machine. It's not a Tin Machine song. I don't give a rat's ass that Reeves played on it either.