Except the Great Bird of the Galaxy (Gene Roddenberry) isn't with us now (shot into space), though you could get Rick Berman, since he was like the XO for the whole TNG-DS9-Voy series. I think all of them have an equal chance of having an advantage. Like with BC vs ST, Trek would win out in terms of sheer firepower, speed, shields, hull, basically everything. But BCs make up in the ability to cloak without that pesky Treaty of Algeron. Not to mention, they have a lot more different types of weapons, and they have a better paint job. Like what's been said, we don't know what kind of effect different technology would have. Like phasers on a BC Shield, it's not known if the Nadion energy would be dissipated or the shields would invert on itself and tear the ship apart.