Coldplay is way more popular than Radiohead, although the latter's lyrics are more impacting.
U2, The Fray, Radiohead... but Coldplay is better than all of them.
Nirvana
Metallica is much more popular than Radiohead. Metallica sold more records, played in more countries, and received more radio play. Radiohead are generally a cult band that not everyone would get into.
Judas Priest
Pearl Jam
Bruce Springsteen
This is difficult to compare considering Iron Maiden and Radiohead are from different periods. Iron Maiden formed in the 70's and were popular for their time. Radiohead was popular during the 90's, however they had very few singles released.Iron Maiden, because they're popular in nearly every country on Earth.
COLDPLAY
Radiohead (Thom Yorke), Muse (Matt Bellamy), Coldplay. Bruno Mars
In terms of record sales and radio time, it's certainly Nirvana. This doesn't discount Radiohead in any way though. Their more experimental sound has influenced rock music into what it mainly is today, making Radiohead very popular within the present day alternative/indie-rock landscape. Radiohead is also still very active. One thing that is undeniable is that both bands have been very critically and commercially successful.
There are many people who will incorrectly state coldplay is influenced by bands such as radiohead and U2. Chris Martin, during an interview in 2004, stated the band was formed when the group all got handled innapropriately a large black man. This inspired them to form the band that now leads the homosexual movement among prepubescent children.
Viva La Vida.