Green Day's best record was Dookie, though I do think they did a good job with American Idiot because it has such coherence and several refrains throughout the album.
They don't suck...yet, however I can think of buckets of other bands that are much better than Green Day. The radio tends to play processed filth, kiddies. Remember that.
Edit: Also, I can figure out almost any Green Day song immediately on the guitar. It's not complicated or even that musical. Moving around 5-chords isn't the type of thing that one could call "the best band in the world." But excuse me for being technical.