apart from blocked cat or f**k muffler the exhaust would make piss all difference to the tune on an NA i6....when i did mine i ran it with just the extractors and cat for a few minutes to see what it would sound like and it ran fine.

Having too big an exhaust size will rob it of power down low, but won't be that noticeable

wow i have got some denial on this one. The exhaust was only the same diameter as standard. Different mufflers were used from when the first visit to the exhaust shops in Taree. as i said it would run but laboured worse and wose as the engine reached its operating temperature. It droaned inside the cab and sounded sh.thouse. Not a nice note I asked for a note only just above standad xr6 so i was not happy with the results. after trying a combination of hotdogs and oval mufflers i gave up. later i changed it for the sytem it has now. A redback. it sounds completely standard only you can hear the air ripping through the muffler like it is very restrictive. The motor starts idles cruses and eccelerates like standard. I would have liked what i asked for but the noise droaning and the change in my car was unacceptable. Dont see how with the standard type exhaust it runs fine but with the louder one it changes ??? ford in Taree just shrugged shoulders and dont seem interested. I find the local ford company a bit disapointing and try not to use them.

CREBERG read my previous post, my car runs fine with stock, modified stock and totally junked stock exhaust and also fine with a 2.5 cat back pipe. The ECU will not compensate the mixture until you are cruising and then I am not sure if it will be able to make it richer which is what you will need with a more efficient exhaust as the idea was to lean it out.
Your Yamaha story sounds a*** about too. The free flowing stainless pipes would have leaned the mixture out. Most noticeable at low to medium RPM under load. Did the idle speed change?
Finally this business of exhaust gas velocity - I think its pretty safe to assume that all things being equal the higher the gas velocity the more force required to get it there. Where is the energy to bring the gasses up to speed coming from? Sure in the scavenging of cylinders etc. the gas flows. pressure fronts and critically the timing of the valves comes into play. However once the gasses have passed the collector, the cat, etc any back pressure is not going to help unless as in the Yamaha case above the mixture has been leaned out expecting a restrictive exhaust system.
Maybe...

The yamaha was confirmed (by the bike shop) to be running rich at idle.It would start dead cold in the middle of winter with no choke or throtle. Mixture was fine for this engine temp. AS the bike warmed the mixture (at idle to low speed became richer and richer and stunk of unburnt fuel. This was evident by black smoke if the bike stalled at idle when warmed up and restarting. the bikes exhaust had plenty of black soot it its end on the stainless 4 into 1 too.The bike, like the car, ran perfect with the standard exhaust. high speed running may have been another thing altogether. different jets and carbrettor styles are affected in different ways so i guess thats what was happening in the case of the bike. as you say the thinking and tech would normaly say it would get lean but maybe it higher rpm only ??

OK what you say sounds like it got richer - I swapped pipes and carbs on my Ducati 750 and a Z900 and mixture always went lean as the pipe(s) flowed more freely. Engine braking changed noticeably too due to the change in idle settings - very noticeable on Kawasaki. Yamaha played with CV carbs and things so who knows.
Check the MAP sensor on your car...

Cheers,
C

my exhaust came loose where it bolts to the back of the cat. i thought i had blown the gearbox and engine because it was running extremely rough (it felt like it) and it would not change gears properly (its a 4spd auto)

everytime i took off from the lights flat footed, the car would not go, it would literally roll off the line. then theres the noise of it all. it was extremely loud.

i bolted it back up again and all was sweet. smooth gear changes and much better performance.

Sounds more like the O2 sensor maybe shagged. With the falcons if the O2 sensor fails the ecu defaults to a safe tune based on standard parts change 1 thing like the exhaust and it wont run real well.

if you put a free flowing exhaust+extractors you may notice a slight torque loss at low rpm wich overall will produce more power, but later in the rev range

otherwise the only way i can see your car loosing power and droning from a free flowing exhaust is its low on compression!