Oh wow, I always thought Twilight 2000 was a module for Delta Green. It looks totally interesting, and they apparently even made a mercenary spinoff of it. I have no idea about the actual crunchiness / mechanics, but it's probably worth looking into. At least I know the sourcebook is going to be interesting.
I'm assuming BRP is the same system that they use for Call of Cthulhu, and all I remember about combat in that is that it's awesome when Ross mows down crowds of cultists with a Maxim gun. I don't know how that'd translate to a modern gunfight with advanced sights, rifles, vehicles, and body armor, but it's probably worth looking into. I remember some actual excitement in the underground fight against the hillbilly cultists in that puppet-people one-shot.
I like over the top combat, but Feng Shui is the only system that will penalize you for NOT diving over a table while you're shooting. I can't imagine a whole campaign of that.
As for realism, it really falls somewhere on that scale. I want it to be closer to John Woo, but not so far in that direction as to be Feng Shui. Actually, I'll just say right now, Shadowrun 3/4 would be my perfect system, I just can't find sourcebooks for the game without elves, dwarves, and implants, and I'm not sure how empty the game would be with all its futuristic stuff missing.
Also I have no idea how to stat out a Predator drone but that is a problem in every system.