With the right aftermarket suspension pieces, you can make a solid axle out perform the pieced-together IRS that came with the Cobra.
Solid axle is better suited for drag duty than the IRS for sure.
When I put in my solid axle I opted for 31 spline mosier axles, eaton diff, 4.30 gears, SVO lower control arms, Mega byte Jr. upper control arms, upgraded springs, shocks, bushings.....it's ready for some serious drag duty. If I cared about auto cross I could have done some things differently to make it out handle the stock IRS.
As for your other questions, yes, the solid can handle sticky tires, more power, and high RPM launches. The IRS's break under these same conditions. The weak point is really the 1/2 shafts. Also, the IRS is famous for the dreaded wheel hop. On the way to the shop I spun the tires and got horrible wheel hop on a cold December day....on the way back after the swap I floored it and just got nice solid wheel spin (stock tires, cold day).
IRS is nice for a daily driver.
Solid is nice if you want a predictable car that sees street and track duty.