The album hasn't technically been released yet, but you can listen to the whole thing on MTV's The Leak here (http://www.mtv.com/music/the_leak/green_day/21st_century_breakdown/#).
American Idiot was definitely a departure from anything Green Day had done before. It was very political, and a lot of fans turned on the band- saying that Green Day sold out, and that American Idiot was a horrible album. Personally, I don't agree. I liked American Idiot, but I liked the older Green Day, too. American Idiot is a rock opera, and it's very political. Musically, it was quite a change from Warning- the instrumentals were layered, and much more complex. Lyrically, it was more mature, and told a story throughout the whole album.
I was pretty excited to hear 21st Century Breakdown. I think it's a good album. Rolling Stone gave it 4.5 stars. If you're expecting to hear Warning, Nimrod, or Dookie, you'll be disappointed. But if you're a little more open-minded, you might enjoy it. 21st Century Breakdown is also a "rock opera", but it's not the sequel to American Idiot. It's somewhat political, but (to me, at least) it feels more personal and emotional than American Idiot did, and less-self-indulgent. It follows the story of Christian and Gloria- possibly the couple we see represented on the album's cover (although the artwork was not actually commissioned by Green Day for the album- it seems to fit perfectly, though). American Idiot had 2 songs ("Jesus of Suburbia" and "Homecoming") that were over 9 minutes; 21st Century Breakdown has more tracks (18 vs. 13), but only 2 ("21st Century Breakdown" and "21 Guns") are over 5 minutes.
The instrumentals are more powerful and resonant than the pre-American Idiot albums, if that makes sense. There's also more use of piano ("21st Century Breakdown"), and I think it works really well. Billie Joe Armstrong is 37 years old now, and Green Day has definitely grown up. Some of the songs are repetitive, and catchy ("Know Your Enemy", "Before the Lobotomy", "Christian's Inferno"). My favorite song is probably "21 Guns".
21st Century Breakdown is a good album because it's definitely not Dookie 2, or Nimrod 2, or Warning 2, or American Idiot 2- it's its own album. It's mature, but it definitely recalls older Green Day. I love that it's a rock opera/concept album. The songs really tie together quite well.
In summary: 21st Century Breakdown rocks. Check it out. If you're a Green Day fan that didn't like American Idiot, you might be pleasantly surprised. If you're not a Green Day fan, you might also be pleasantly surprised. If you're a Green Day fan, you might be pleasantly surprised. If you've never even heard of Green Day, you might be pleasantly surprised.