The ta/camaro and mustang were purpose built for a different market. Its simple, don't get "sandy", as you put it, because that's just the way it is. Of course you can build up the suspension, handling aspects of any car and it should perform well enough. Like Space said, it really comes down to the driver. Though here's some numbers to digest for stock form, all other things equal, those cars are definitely at a disadvantage.
For a direct comparison of the 350z vs a gt mustang go ...
http://www.motortrend.com/roadtests/coupe/112_0506_compact_sport_convertibles_comparison/index.html
Or an STI and a GTO
http://www.edmunds.com/apps/vdpcontainers/do/vdp/articleId=105773/pageNumber=1
Compare the Skidpad, Slalom, and Braking between an EVO, a WS6, and a GT.
http://motortrend.automotive.com/39854/112-0411-2003-mitsubishi-lancer-evolution/specs-overview.html
http://www.motortrend.com/roadtests/coupe/112_9912_2000_pontiac_firebird_trans_am_ws6/index.html
http://www.motortrend.com/roadtests/coupe/112_0411_2005_ford_mustang_gt/track_test.html
Driver mod is still most important regardless.
EDIT: fixed