My comparisons are purely from the live performances. I have not listened to 3 or BTBAM albums. Would the phrase 'completely kicked their asses on stage' be any clearer for you? I think you know exactly what I mean when I say that a band was blown off the stage, think you are just trying to be awkward!

Dude you are talking jibberish to get a point across with all that wine crap!
3 were like a completely new experience, exciting and very mood driven music with some amazing acoustic guitar played in a way I have never really heard mixing with a heavy band before. Totally exciting.
BTBAM seemed at the time like a bunch of kids, the singer was screaming like an emo whilst walking backwards and forwards in flip flops to his keyboard and played some very uninspiring parts. The guitar player was great but they seemed like they were not all that great but they had the best guitar player in their school in the band! 10 mins in and most people went for a **** break.
Opeth where amazing and poor at the same time. Some great vocals and awesome segues with incredible melodies that then went into bog standard generic shouty metal that I had heard and since grown out of 15 years ago. Enjoyed in parts - the most enjoyable parts was the singer talking and telling stories in between songs. The missus actually fell asleep watching Opeth - how rock n roll is that!
Dream Theater stole the show with their precision, interaction with fans (apart from Myung!) just the way they controlled the stage, plus ofcourse the extras that support bands dont get - extra volume, lighting screen etc.
I am a huge Dream Theater fan and thats why I bought the ticket, so you could argue that I am being biased - but after seeing billions of bands, the 3 DT shows I have seen are the best of the lot.
The other bands were the first time I have seen any of them live - so they all had a fair start to impress!
I wouldnt in a million years say that BTBAM and Opeth produce more complex music than DT... not that that matters, as you say. Maybe they do play more complex stuff on cd but they didnt have the balls to play it live which is where they differ from DT.
Maybe I can get on board with your wine talk if I am sitting down to listen to a new album... me, the couch and the sound system, as you say right mood and time etc. But in a live sense you just have to throw that wine down your neck and see if it kicks your butt!