Can anybody tell me why the amplitude goes down by half?
Your circuit has differential inputs and outputs which are balanced with respect to ground. However you are only measuring the output on one side, so you only see half the voltage (-6dB). To get the total output you need to measure both sides and subtract one from the other, like this:-



The sharp peak is caused by resonance in the LC filter. It will be reduced if you add a realistic load impedance.