The theory is that the BOV allows to compressor to keep pumping during gear changes and times of closed throttle.
On full boost and WOT, the air from the turbo compressor is flowing into the engine. During a gear change, the throttle snaps shut, blocking off the path for the air into the engine. However, the compressor keeps pumping. Eventually it will reach the limit of its capacity to pump air and start to slow down. So when the throttle opens again, the compressor needs to spool up again.
Now, if you release the pressure, via a BOV, the compressor can continue to work at optimal performance. So when the throttle opens again, the compressor is still at it's optimal speed and pumping capacity, gaining immediate response from the engine.
I'm sure if BOV's detracted from perfomance, the manufacture's would not have invested millions of $$$ developing the engine with a BOV attached.