Well, I liked the concept that Cisco of The Advent did of calling some of his remixes which had very little in common with the originals "remakes". Not only does it sound cooler, it dignifies the work of the artist who did the reworking much more than "remix" does, which implies you're simply rearranging predefined elements.

As a remixer, the concept of completely rebuilding the track into something different is very appealing despite being more work than a simple retread. As a record buyer, being able to buy a record with one track plus remixes and effectively get 4 unique tunes out of it is also a better bargain than a series of mixes with the same concept and layouts. To me a good remix should have at least one familiar element from the original tune while creating a different mood or perspective. Cross-genre remixes are especially interesting as well, such as the Kraftwerk Expo 2000 remix series that came out.