The technical term for a straight through muffler is "pipe".
There should NOT be a huge difference in performance. The muffler does present a flow restriction to the exhaust gas - a muffler makes the flow change direction through various sized holes, which disrupts the sound also carried in the exhaust. Any change in direction must necessarily change the velocity of the gas, particularly through the smaller orifices inside the exhaust. When you change the orifice size, you increase the velocity through the orifice and increase the pressure behind it - that's the flow restriction in operation.
However the flow's already restricted enough by the CAT/DPF, but moreso by the turbine. The opening into the turbine chamber is quite small (relatively speaking) so that the gas velocity rises. At this point you WANT a higher velocity, to spin that turbine. As the exhaust leaves the turbine blades (expending its energy on the blade rotation) it loses quite a bit of energy. Because the turbine outlet is larger, the flow rate can slow down, but the exhaust gas temperature (EGT) at that point also drops anywhere between 150C and 300C depending on throttle, RPM, load, turbo vane setting etc.
After the turbocharger just off the dump pipe is the CAT. This is also a flow restrictor but it has minimal impact on engine performance. Further back (and having even less impact) is the DPF. Lastly the muffler - which will have a very little impact on performance.
That's the "why".
As for the noise, it WILL be different (explained above). Whether it's to your liking is hard to say. Getting a nice note out of a turbocharged engine is difficult because the exhaust gas is all compressed and passed through a single, small orifice which munges the sound. The lovely sound you get from a V8 comes partly because two banks of cylinders are run through separate exhausts.
Some of that sound is induction noise too. I took the air intake pipes off my XJS Jaguar (5.3L V12) and it made a gorgeous sound. I've removed the baffles from my Navara's intake and all it does is rattle lots, although my turbocharger is very clearly audible now. I will be putting the baffles back - I don't like the rattling sound.