I've never heard an Alter Bridge album, but the few songs I've heard sounded good. They have a modern sound for sure, but also have a bit of a classic rock sound to them.
They have that modern almost alternate sound, but Myles has a lot to do with that. He's not really a metal vocalist. But a lot of their stuff is some of the heaviest shit out there. Great unique mix of styles. Some of their songs would appeal to you guys but some would certainly be hit or miss.
I'm a huge fan. My wife and I can't go to shows together right now (no sitter), but we're both hardcore AB fans, and she went to our local show a few nights ago. They played a great set. I've seen them four times (1x on Blackbird, 2x on AB III, 1x on Fortress), and they were outstanding. As for the records, wolfking is pretty much dead on.
They are a great mix of classic metal, thrash, hard rock, and alternative rock styles. Borderline progressive as well, the way they alternate tempos/moods in the songs. For those looking to check them out, I always say, start with the Blackbird album. The title track is a real nice moody epic with a killer trade-off guitar solo that DT fans, fans of classic Queensryche, would dig. So many great tracks on that record - Wayward One, Ties That Bind - it really is good. Fortress, would be my second pick for people. I think that record really showcases their diversity pretty well.
I love all of their stuff, honestly. AB III is really dark, thematically. So if dark stuff is your thing, give that a listen. Slip to the Void, Isolation, Words Darker Than Their Wings, Show Me a Sign -- all just killer stuff.
Myles, in addition to having operatic range as a vocalist (think Cornell, but a bit sharper at times, with higher range), is a killer guitar player. He and Mark Tremonti work really well off one another. Think DeGarmo-Wilton if you're familiar with Queensryche. Myles cut his teeth playing jazz guitar and teaching guitar, and while he can shred with the best of them, he's very much someone who likes to put a lot of feel into his solos. Mark is a shred MONSTER. Combined, it is really a beautiful thing to listen to. Perfect contrast without seeming out of place.