I think you guys are arguing semantics. Acceleration is proportional to torque at the wheels, and it can be calculated by area under the torque curve. HP is a calculation from torque and speed.
The car with the greater area under the torque curve will win. Generic comparisons of "500HP versus 500lb-ft" are meaningless without comparing RPM - where the engine makes the torque, and how flat the torque curve is.
So for the generalized 500HP with turbo or supercharger, we have to assume a few things: turbo makes full boost long before rev limit, where supercharger typically makes full boost at rev limit (and significantly less boost below the rev limit if it's a centrifugal blower). The extra mid-range boost from the load-based turbo increases torque output, and should have the larger area under the curve.
At the BMW CCA Oktoberfest club race at Barber Motorsports Park in Birmingham, AL, a 135i in H-Prepared would literally stomp all over higher HP mod-class cars exiting the turns due to its massive torque over the naturally aspirated competition. Once the NA cars were in the higher revs where they finally made some torque, they were able to stay the same speed as the 135. If the drag race were to continue down a runway (they were limited to the short straights at Barber), the higher HP cars would start to reel in the 135 due to drag. Higher HP is desired once aerodynamic drag comes into play.
E92 335i/6MT Dinan Stage 3: intercooler, oil cooler, intake, flash, exhaust, LW dual-mass flywheel.
Vishnu PWM methanol custom trunk mount, Diffsonline 3-clutch Salisbury custom diff, Ohlins Road and Track coilovers, Vorshlag camber plates, much more...
E28 M5 w/ buncha stuff, R171 SLK350