Whichever ones have the better tactitions on board.

Honestly though, I don't think this is necissarily an answerable question.  It's like asking which would win between relatively equivalent ships from Star Trek, Star Wars, Babylon 5, Battlestar, Firefly, Star Gate, FarScape, or any other story/series/game/etc.  You generally just end up with people choosing whichever is their favorite and explaining why.  The biggest problem with any comparison from different 'worlds' is that there tends to be no true base to compare by.  It's pretty much all relative and subject to personal interpretations.

Now, if someone could actually create a solid base to compare from between any given world, and get all the respective sides to agree on it (..yeah...RIIIGHT.  Good luck on THAT part.), then we could easily geek out to our hearts content on figuring out who can beat who, in which fashions, and under what circumstances.

We're dropping an andromeda ship into the sins world here.  A Commonwelth Officer would never launch a nova bomb into an inhabited system.  Besides, would Slipstream even work here?  If not, it would be suicide.

Still, i think a DSX Attack Cruiser like Balance of Judgement or Wrath of Achilles would own any capitol ship, since the thing is essentially a massive armored missile silo.

btw, how do you post a link to a pic?  I can't just copy and past for some reason.