SM & Queen were there first rivals. Both throughout the 80's.
Some bands had short periods where they could claim they were bigger.
The Police were the biggest band in the world in 1983-1984 and overall the biggest band of the early 1980s worldwide. So in that respect they should be on the list, even though they essentially broke up after 1984. Simple Minds were never big enough in the United States to qualify for this list. What popularity Queen did have in the United States evaporated in 1982, with a poor selling album and poor selling tour.
In general though, Coldplay is the only band that really challenged U2 commercially and for public appeal for a considerable length of time and managed to unseat them from their throne about a decade and half after they released their debut album. R.E.M. challenged U2 for a bit in the early to mid 1990s, R.E.M.'s most commercially successful period.