I've raced the Miata for several years now, got it dialed in EXACTLY the way I'd want it (slight understeer for quicker transitions), and couldn't love the car more. BUT, the Cooper rolls more?!?! I don't think so. The Miata has a lower center of gravity, but a silly putty chassis compared to the Cooper. If you drove a Cooper with the 175/65's on it, I can see your point. I've now run a Cooper with 205/50R15 Kumho Victoracer V700's and a Cooper with 205/45R16 Kumho Ecsta V700s on it. BOTH had less roll and stiffer chassis dynamics than my 10AE, which I've run at Nationals on both the Kumhos and Hoosiers. All I need to do is dig up the pictures of both cars around turns (if I can find my Miata pics).
Why would you compare a Cooper to a Turbo or Supercharged Miata?? Compare a base Cooper to a base Miata, or a Cooper S to a 10AE, but not a normally aspirated Cooper to a forced induction Miata.
I could've agreed with the FWD vs. RWD idea, but not after I autocrossed the Cooper. The most fun I've ever had squaring of the corners

. Now, going around a sharp 90 degree turn and squeezing on the throttle doesn't give you that fish-tale-fun. But I was in the Cooper for five minutes before I went into a U-turn and had the car completely sideways.
They are two completely different feeling cars and it's certainly an opinion issue. But, having driven both cars to their limit on R Compounds, I'm confident I made the right decision.