Just to clear up a few things, there are 3 "cans" down there.
The first (closest to the turbo) is the NOx catalyst. It's in the downpipe and is kinda flat and wide. To get the downpipe out you have to take off the tranny support member.
The second is the oxidation catalyst (aka DOC). This is big and round and in the straight section of the pipe.
The third is the DPF, also big, round and in the straight section.
The main restriction is from the DPF. This is because in the DPF the exhaust actaully has to flow through the walls of the ceramic honeycomb. In the NOx cat and the DOC, the exhaust just flows through the channels, but not though the walls themselves. That being said, they still add some backpressure.
The way I figure it, if you're down there taking stuff off, you might as well take it all off (that's what I did). Taking the downpipe on/off is a little tricker because of the tranny support member, but not that bad. If you don't want to do that, you can just take out the DPF & DOC. Most kits have one delete pipe for the DOC & DPF, and a separate one for the NOx cat (downpipe). At least that's how the one I got was (H&S).
As far as the sound, I thought it sounded pretty much the same before and after. As long as you don't delete the muffler, I don't think anyone will notice any difference in sound.
'07.5 2500 ST, 2wd, QCSB, G56 6-speed manual, 3.73 gears. DPF, EGR, IAT, CCV, NOx Cat deletes. Smarty Jr FE tune w/ most adv timing. Homemade ram CAI, Upper & lower grille block, tonneau cover, Dual 150W oil pan heaters ~Fuel mileage obsession~