On the GT500, see if you can drive one that has suspension mods and is more dialed in. From factory they weren’t comparable to IRS. Frankly, they’re not confidence inspiring
I put a watts link in mine (cortex) and everyone who has driven it that has come from an S550 has been amazed. It still wants to kill you but it will do it with so much more precision
I think the comparison of a stock GT500 to a GT350 may be unfair otherwise
A Gt350 is in a totally different category in driving from a GT500. I had a 11 with a lot of 13 parts, and I can tell you that it was in no way able to outdrive my 350. The only thing it had over my 350 was raw acceleration, straight line speed. Now maybe a GT500 with watt's links and other mods may do the trick, but you can as others pointed out drop F/I on the GT350 and be in the same position.
I know of several F/I Gt350's and man.....yeah they are fast and can still turn a corner. Honestly if your looking for that blower feel, and want the newer platform, then a GT350 with any of the F/I options will do just fine. I would lean more towards a Procharger or Turbo option...but that's just me.