From what I have read, the crossover is supposed to improve scavenging at low to mid rpm's.
As each cylinder's exhaust pulse goes down the pipes there is a positive pressure in front of the pulse and a negative pressure following the pulse. As these pluses pass the crossover the positive pressure ahead of the pulse passes through the crossover it can't go back up the other pipe, valve closed, so it helps push the exhaust out of the pipe.
The negative pressure behind the pulse crosses over and helps pull exhaust out of the head when the exhaust valve opens.
These negative and positive pressures alternate side to side as the engine runs. They only help at lower rpm's because at higher rpm's the exhaust if flowing fast enough so the effect is very minimal.
An exhaust engineer may have charts and tables that can show how much effect this scavenging has, but for us on the street can we tell the difference, I can't.
My buttdynometer isn't that well calibrated.
Leo