In either case, you aren't getting the sense of movement that a chord line usually contributes to a rock song. The difference is more a matter of texture than structure: the chord instruments get to play something instead of staying silent.
While it's quite rare to hear a whole rock song with no chords, a song with only one chord is only slightly unusual. There are thousands of them in all different styles:
- funk and hip-hop songs with tasty grooves that just keep on grooving
- blues songs that eschew the "12-bar blues" formula and just stay on [one]
- ambient and electronic pieces where sound textures create enough interest without the need for chord movement
- folk- and tribal-influenced songs with strong, active melodies
Some great examples of one-chord songs are "Electric Avenue" by Eddy Grant and "Punk" by General Public. In both cases, a well-crafted arrangement keeps things moving, so you might never realize that the chords aren't going anywhere.
What are your favorite one-chord songs? Please list them in the comments.