Between the FIAT and the Mazda I do not see a lot of difference. As you say they should be close to identical for quality with the engine being the decision. I would however go for the Mazda on the grounds that the supporting dealer chain will be far more experienced and possibly better. In the UK FIAT have had a rough time outside the 500 so engineering experience and availability of FIAT dealers would be a thought?

If you need to look at alternatives then autotrader is your friend. Open a search and choose the more options button.

Petrol
2 seats
less than XX miles (lots of pre-reg and nearly new stuff saves money)
less than xx years
budget min/max
Any other things ?

Then take some time paging through.
Its always good fun on an idle sunday.

Everyone loves a Morgan. Even me, unless it's broken again.