Well, I've been running a Nailbomb in the bridge of my Les Paul quite a while, and with some amp tweaking, it hit the Alter Bridge sound very well. Also sounds very nice for the clean sections, plenty of 'life' (that's the only way I can put it).
I only got the Bullets and Octane album a couple of weeks ago, but my inital take would be that you might want something a little less hot, a little more vintage voiced for that kind of tone - from the description on the Products page, something along the line of a Black Dog perhaps.
Please note, that's only based on what I've read, and shouldn't be taken as any kind of gospel.
