Fortress and Blackbird are the best.
Fortress is the proggier album. Its so dynamic, not really any filler, other than Cry A River, and the production is the best of all the AB records. Some of the best vocal work from Myles on here, the riffs are simply off the charts and I love the darker vibe of a lot of the songs. Also, Cry of Achilles.
Blackbird is just a rock masterpiece, and it has Ties That Bind, Watch Over You and Blackbird, some of the best tracks the band has ever wrote. The true introduction to what Alter Bridge is; every track has something special about it.
ABIII is in 2nd, but not too far behind.. I adore that album but its unnecessarily lengthy. If certain songs were cut, it would be tied for first. I like the bsides from ABIII much more than a couple songs that actually made the cut, but those sides are damn good songs in general. Words Darker Than Their Wings is half the reason I love this album so much.
ODR is a great album, but like others have said its really kind of a very Creed-esque album. It really is a beautiful piece of art. Plus, Myles voice was in top shape on this record. Every song belongs, I personally dont see any of it as "filler", which is not true for the other albums. Each track belongs, all of them are awesome in their own way, but its not really AB as we know it.
The Last Hero is last. As much I want to love it, I just dont feel a connection like I did with the other albums. The highest amount of filler, and it seems kind of unfocused if Im being completely honest. Its not a bad album, but it isn't great by AB standards. Its just good, with a little bit of great thrown in.