When I referred to the song as being by Echo and the Bunnymen, a coworker informed me (with some condescension!) that it was actually by the Doors. I picked up a Doors album at the mall the next chance I got, and they immediately became my favorite band.
Listening to the Echo and the Bunnymen version again after all these years, I think it still holds up as a good take on the song. The extended instrumental interlude is reminiscent of the Doors without being a slavish copy, and some of the variations on the original are musically interesting. A good cover doesn't just copy the original note for note, but nor does it make a mockery of what the original artist was trying to do. The Bunnymen walk that fine line in this version, and they do it successfully. Echo can't really walk any fine lines, because Echo is just the drum machine- but it does a good job too!