There is quite a fundamental difference between the two.
Technically gelato is churned at a much slower rate so there is less air in the mix, it’s usually a milk base rather than cream (and eggs), and rarely is the base made into custard before churning. It also tends to be served slightly warmer because its denser (less air).
But what does that do to the taste. The texture of gelato is often chewy, in fact when its put in a cone/cup they use a scraping technique because its so sticky. It also tends to give a more intense flavour because you don’t get the fatty/luscious texture (which coats your taste buds) you get with ice cream - hence the myriad of flavours that are available in Italy.
I don’t think one is fundamentally better than the other, they are simply different. You can also add sherbets, sorbets, granites and frozen yoghurt into the styles available.
Why is Gelato so fashionable? I think its because its quite easy to make, the commercial Gelation machine is a bit like the soft serve machine - put the ingredients in, switch it on and it produces and can produce small batches. Ice cream is technically more complex with good quality ones needed a custard base. So buy a few machines and display fridges and your in business selling scoops at $3 each…hence the proliferation of shops.