The main factor to the "bad" sound is the design of the turbo manifold. The stock manifold is a cast iron log style manifold with very short runners and exhaust pulses that merge as soon as they leave the cylinders. If you listen to sound clips of cars that have tubular style manifolds you'll see that the sound is alot cleaner and higher pitched but also more agressive. The Barra GT350 from Adam LZ's videos also has a tubular style manifold which gives it that sound you notice.
Take a look at this video of an XR6T with a 6boost low mount manifold
https://www.youtube.com/watch?v=a7rFqr-HUfE