the back box could lose you power, all to do with back pressure.. but cant see a decat losing you power.
all here..
Performance exhaust systems are designed to increase the ability of these exhaust systems to flow a larger volume of air with less restrictions. A less restrictive exhaust system will generally result in more power up to the point at which there is enough back pressure to allow the vehicle to run properly. Back pressure is a measure of how restricting the exhaust system is to the used exhaust gases moving backwards in the exhaust pipes towards the engine. If an exhaust system does not provide enough back pressure, the engine may actually pull used exhaust gas in through the exhaust valve while it is still open during the beginning of the intake stroke. This would contaminate the fresh air-fuel mixture entering the combustion chamber and reduce the power generated by combustion. The point is, that there are limits to how large a performance exhaust system can be, before the "performance exhaust system" will actually start to rob horsepower (not to mention creating running problems).