Cats restrict power: Proven difference.
Back in my hot rod days, On my 94 Z28, I removed the cat and the car FELT noticeable faster.
However, I never took seat of pants or sound as seriously as most. I would always take the car to the track after a change not to race people but to test/see if it REALLY made a difference. In this scenario it turns out the seat of pants indicator was correct. After numerous runs all thing being equal, I consistantly ran 2 tenths better during the quarter mile run with the cat REMOVED(13.8's to 13.6's). About 2wice as loud though. Great on a american v8, not so sure it would sound good on a 6cyl or diesel although a turbo diesel may not be as loud as normally aspirated diesel..
Basically, in the 94' Z28 5.7liter eng. with 275 factory horsepower this equated to approx 20hp difference based on quarter mile times and other factors. I do not know if all cats are made equal and on smaller engines there may be quite minimal difference and too much loss of low end to even matter. I guess on that car I didn't feel much loss in low end considering it put out 325ft pds torque @ 2000 rpm in the automatic.