I think they are both great cars but have only driven the MR2 on the track so dont really know what they are like on the street. I have been taken for a drive(MR2) on two occasions and found just being in the car far more of an experience, it has far more presence than a MX5. The MX5 is a nice car having my GF at the time own one in 98 which I would take out for drives, pick up the kids, but it was always a bit of a joke, gay some might say..
Also drove one at the Wakefield 300 a few months ago in pouring rain for 67 or so laps. It was a complete blast to drive as it had dry weather semi's,locked diff and bad brake bias driving with minimal visability. Very difficult to keep in control managing sideways on every corner, 3 360's, 4 drive thru's with gravel traps, aquaplaning constantly. It was a really fun car to drive over the limit all day but there are limits.
I have also driven the MR2 in the wet which was a different experience. The Mr2 is closer to a go kart type handling than the MX5.
Neither is better as they are different cars so it comes down to what do you want to experience. If you like a FR car, take the MX5 or a Supra. If you dream of the engine screaming right behind your shoulder, look at the MR2.