I will defend the old Camaros to the hilt because I had one and after 4 years I'm sorry to say it had personality by the shedload and I loved that car. By contrast, the Corvette C5 Z06 and my blown 05 are far more anodyne but the reason for that is they're so damned capable that it's much harder to have any real fun.
However, before you beat up on your Mustang too much, the two cars weigh much the same and it's an open secret that the LS1 put out far more hp than GM ever admitted because they wanted to distance it from the Corvette. When MM&FF tested the 2002 SS, it was supposed to put out 325hp but it put out 317 at the wheels which makes that tranny a very efficient unit! There had been a dyno test in 1998 comparing a stock TA with a stock C5 and it was the TA that put out more power to the back wheels (but of course it weighs more than the Vette). If you think about it, why would GM have to spend more money to detune an engine that rolls off an assembly line at a rate of knots. I suspect they didn't, just controlled it via the computer.
The major difference between the two cars is handling. In stock form, the Camaro SS is a reasonable car but can be squirelly at the back end and nowhere in the same ball park as the Mustang. This is because the T-tops make it your flexible friend and of course many of the outer panels are plastic with no structural function. On my old Z28, I had to have subframe connectors welded in and a strut top brace fitted to stiffen up the body and these add weight but partially cure the floppiness. The 2005 Mustang is incredibly stiff to begin with so has an immediate advantage.
I still have fonder memories of my Z28 but that's probably because I drove it more as a daily driver whereas my Stang is more a weekend car. I also think the T-tops made it a different car for different days.