Writing great, original songs is an amazing skill. The creative artist(s) at his/her/their peak. But making alternative versions of existing songs can lead to equally amazing results, especially if the new version is not simply a cover, aiming to replicate the original as closely as possible, but rather an individual interpretation.
In my experience, some of the best results are linked to a switch in genre between the original and the new version. Take for example Nouvelle Vague, a french band that has released some albums with bossa nova versions of new wave classics – some of them absolutely wonderful, like Blue Monday.
For those not familiar with the New Order original, released in the mid 1980s as a legendary 12″ vinyl maxi-single that looked like a 5 1/4″ floppy disc (if you have no idea what those are: consider taking a crash course on the 80s), here is the original as well.