No way is it better than Exile. It's a great album for sure, but it's not better than Exile. In fact I'd say it's not in the same class as any of the big four - Beggar's, Let It Bleed, Sticky Fingers, Exile.
To me it belongs in the next tier of Stones albums - classics, just not as good as the big four (and really, there aren't more than a handful of albums by any artist that are as good as the big four). I would rank them this way (studio albums only):
The Big Four
1. Sticky Fingers (by a nose)
2. Exile
3. Let It Bleed
4. Beggar's Banquet
Classics
5. Some Girls
6. A Bigger Bang
7. Tattoo You
Lesser Classics
8. It's Only Rock 'N' Roll
9. Bridges To Babylon
10. Black And Blue
11. Voodoo Lounge
12. Dirty Work
The rest are hit and miss IMO - about 50% songs I like and 50% songs I don't care if I ever hear again.
That they can even make an album as good as A Bigger Bang in 2005 is amazing. It really does hold up well under repeated listenings (all except Streets of Love, the one song I don't like; I burned a version of the album without it). A Bigger Bang is a classic and will be regarded as so 30 years from now. I have to make sure I stick around 30 more years so I can gloat when I'm proven right!