FWIW, I have spent a fair amount of time at Miata.net, where they have a VERY active forum (more than 19,000 members and lots of discussion), and this topic has been kicked around quite a bit. There are strong opinions on both sides. Some general observations:
If you have an oil leak, it *may* be more noticable with synthetic.
If you tend to stretch out your oil changes a bit, use synthetic.
Synthetics are recommended for *extreme* conditions or very cold weather.
If you change oil regularly and often (say, every 3,000 miles or so), dino oil is probably just fine for you.
Some people believe their engines actually run more smoothly with synthetic. Maybe so.
If you don't mind the additional cost, give it a try; it can't hurt and you might like it. If you want, you can always go back to dino.
I may have missed a thing or two but there's the basics. As always, YMMV