There are a number of books that explain exhaust "tuning". From what I remember, the exhaust pulses in tubing can be likened to sound pulses. When they reach the end of a pipe a shock wave is created and it travels back up the pipe to the exhaust valve. A properly designed crossover pipe will be tapped into the other side at a point where the returning shock wave is bled off to some extent, reducing the shock in both pipes because of its phasing. The returning shock wave inhibits exhaust flow. A good example of the design intended to reduce the shock wave at the exhaust exit can be seen on motorcycle mufflers that have a megaphone shape (allowing the exhaust to expand and weaken the shock at the end of the pipe) and some have a small reverse cone that excludes a percentage of the return wave.
I think the effect is greater on smaller engines, that the larger ones have enough pressure and volume that the sound-like shock waves don't have such a proportionately large influence. There are motorcycle engines that just won't run without the proper muffler or pipe-end shape.
Length and diameter are influential as well: narrower pipes result in higher exhaust speeds and more "tuned" effects; longer pipes favor torque, shorter for HP.
I remember some of the Trans-Am Camaro racers of the late 1960s or early-mid 1970s went with "180-degree" headers where the exhaust pipes met in the collectors at specified pulse intervals depending on firing order, actually crossing from one side of the engine to the other side for collection. They sounded like - what? - high-revving engines with more than eight cylinders. I seem to remember they fell out of favor because the HP curve was peaky, when heavier cars on road courses were better-off with proportionately more torque. Installation and removal made engine maintenance difficult, as well.
All that stuff is probably available on-line somewhere. Some of what I remember may be off-base.
On my current V-8 cars I have replaced the mid-section of the exhausts with FRPP "X-pipes". It seems to me the change in performance was an increase in horsepower at higher RPM: you get up there five thousand and higher, you can feel it and hear the exhaust lose its V8 "thump" and begin that screaming sound. Mmm mm. I like it.
I don't know what "raspy" sounds like now, as everything from about 3.5KHz on up is gone from my hearing.
My sense of the crossover versus straight back is that the straight pipes will sound pretty good to everyone, but they are not allowing the engine to do all the power-production it is capable of.
