Since punter got it handled with the twincharging questions. I'll just comment on this.
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Originally Posted by freakinbox
this was covered in initial d with 2 rx7's lol. I swear that show has the answers to everything car related 
- Ok big turbo is more laggy, but more powerful. Also they will be more smog legal. usually 1 larger turbo rather than 2 smaller ones
Twin turbo is more resonsive, but weaker than a single turbo. Will be harder to keep smog legal.
Super Charger is the most responsive since it's belt drivin. Not as much torque compared to a turbo and it will burn more fuel then if you turbo it. But it's the closest to the responsiveness of an N/A motor that a forced induction motor can get.
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Some of things you said are correct, and other parts 1/2 right.
1) A larger turbo will create more turbo lag.
2) There are 2 different methods of going twin turbos, sequential systems and bi turbo systems. A sequential system runs a smaller turbo and a larger turbo inline to get the best of both worlds (mid range and top end). A bi turbo system involves 2 identical turbos feeding to different cylinders.
3) There are different reasons for going with different turbo setups.
a) A single large turbo can make lots of boost up top to make lots of top end power, this option is generally only good for drag racers since the powerband is very narrow.
b) A single small turbo gives you quick spooling low end, but these turbos will run out of breath quickly giving a weak top end.
c) A single medium sized turbo, compromise between a and b.
e) A bi turbo system can produce a wider powerband than a single turbo of similar power output. Usually built for a very powerful mid range and decent top end.
4) A supercharger creates the most amount of low end torque because unlike a turbo, it does not need to be spooled (altho rpms still affect how much boosts a SC can produce). Superchargers are the best option for people seeking low end torque. However, superchargers are generally not as effecient as turbos (meaning they blow hotter air sooner), making turbos a better choice for top end seekers. A supercharger doesn't always produce worse gas milage than a turbo setup, it really depends on the tune and setup of the vehicles.
I don't understand your smog comments... what does the number of turbos have to do with passing smog?