I've just changed out the Big Shot Longs with quiet baffles for a D&D Fatcat with quiet baffle. My bike is an '06 Heritage Softail Classic with a stock engine, other than the Stage 1, K&N air filter and a PCIII USB.
I won't know the real numbers until Saturday, when I've scheduled a dyno (I will publish the dyno results when I have them), but after 200 miles I can say that the butt dyno tells me I'm riding a different bike. I've never felt this level of acceleration on this bike, both from a standing start and with a 5th gear roll-on at 70 mph.
The V&H dynoed out at 71.1 hp and 74.3 ft-lbs torque. It will be interesting to compare the two. I'm guessing as much as a 10% increase, but what do I know. It'll also be interesting to see where the power comes in.
As to sound: the V&H with quiet baffles are NOT quiet. They sound a little louder than the Rush pipes with the 2" baffle I used to have. The Fatcat IS quiet, yet with a very nice rumble at idle and a distinctive roar at WOT.
As to looks, that's very individual, so you'll have to judge for yourselves. My take is that the BSLs look smoother and more nostalgic, while the Fatcat looks very aggressive.