Barring flatlines or other barrels that impart backspin, ALL barrels will shoot shoot the same paint the same distance, given the same velocity.
Accuracy is determined by
fresh, round paint,
a decently honed barrel (which is most of them these days)
Buy whichever you like best.
DYE barrels are very nice, but generally more expensive than equivalent barrels.
I don't know anything about the Empire twister, but as long as it's not one of those adjustable bore fiascos, I'd imagine it's perfectly decent.