A car with 3.55 will get off the line better, if he can get traction.
That is because the 3.55 car has more torque to the rear wheels in first gear because of the mechanical advantage of those gears.
As you go up through the gears there will be points where the 3.55 has an advantage and points where the 3.08 has an advantage.
This is because the overall gear ratio, trans and rear, changes with the shift points.
The only change in the horsepower will be due to the increase in gear friction loss in the 3.55 and that is probably not much over the 3.08.
You can increase torque with gears but you can't increase horsepower with gears.
Horsepower is calculated by measuring torque and rpm.
When you increase torque with gears, you reduce rpm and so the formula will give you the same horsepower number.
In other words, you don't have more horsepower at the rear wheels at 5000 rpm in first gear than you do at 5000 rpm in second gear.
You have more torque at the rear wheels in first gear at 5000 rpm but the rear wheels are turning slower than in second at the same 5000 engine rpm.
Any dyno that shows a change in horsepower because of rear end gear ratio change, is only showing an artifact of how that dyno makes it's measurement.
This is aside from the small loss due to increased gear friction.