They both handle well enough... I would give the edge to the GTM for potential for sure. Much more rigid frame and sophisticated suspension. (GTM is born of a C5, compared to a older mustang/t-bird for the cobra)
The roadster NEEDS either 3 link, or better yet the IRS to handle well. The GTM comes with IRS stock.
Really, the biggest question you should be asking yourself, is what kind of car do you want? They are completely and totally different animals. Both can be made to handle well beyond what anyone should be doing on the street with really good manners.
The GTM will cost roughly 2X what the roadster will cost to build and probably 2-3X the time to build it. With that, you get a relatively modern feeling car with AC, Heat, Power Windows, Tilt Wheel, etc... The Cobras, while they do gather attn, its NOTHING like the GTM. The GTM gets more attn than pretty much any exotic besides and Enzo, or Veyron.
David