As a big Green Day fan who has grown up with this band on my stereo (and the first band I truly loved as a teenager), I approve of this compilation. Most of the big songs are here, in chronological order, with a few bonus items included. These include the pre-major label highlight "2000 Light Years Away", a version of "Ordinary World" with added vocals from Miranda Lambert (which I just happen to prefer over the original) and a good new song in "Back in the USA" (it is not a Chuck Berry cover, heh). The cover art is also nice, so maybe I will get this on vinyl one day.
If I have to nit-pick over the song selection, this would be it: I think it's a bit disappointing that "When It's Time" isn't on here, since it never got the attention it deserved. Some of us European fans that came late into the game (that is, when "American Idiot" was released) got introduced to the non-album single "J.A.R." through "International Superhits!". Had "When It's Time" been included on "God's Favorite Band", it could have gotten a wider exposure the same way, which it deserves. "Waiting" should also be here instead of "Warning", since, unlike "Warning", it is still being played live regularly by the band. It is also strange to hear "Brain Stew" without its second part "Jaded". It's only 1:30 long, so it would have fit as is. Lastly, I would personally have no problem with trading "She" for another track from "Insomniac". But that really is a personal preference, and "She" is a great song. I understand why it's here.
Nit-picking and personal preferences aside, "God's Favorite Band" in the end effectively replaces "International Superhits!" as the preferable compilation. If you're a newcomer to Green Day, there is no better place to start than here. I do strongly recommend "Dookie" and "American Idiot" on their own, however. I say start with "God's Favorite Band" and then explore on your own.