I had a Punto HGT as a daily a few years back, and my other half has owned 2x MX-5 mk1.
The Barchetta is based on the Punto floorpan, has the same engine and gearbox, and probably shares a lot more than just that.
I can say with 100% certainty, that'd I'd buy a mk1 mx-5 every day of the week before the Barchetta (despite the Barchetta being the prettier car).
The build quality on the Mazda wasn't amazing, but the Punto felt like it would fall apart. The electric power steering on the Punto was vague and unreliable, the mx5 was a hoot with average tyres and a decent geometry set up.
I think the mx-5 mk1 is a beautiful car. It has the classic British sportscar look about it and still looks great today.
The whole mx-5 is girly thing is getting very old. It was bought by everyone, including woman, simply because it looked good, the roof came down and it was cheap. I honestly think Mazda really got it right - then ruined it with the bland mk2