There's quite a big price difference between the housings...
Of course the Nauticam is a better housing - better material, smaller, 67mm thread etc.
But with the price difference of the Fantasea housing you can afford a wide angle lens for the same price, which means very good value.
Fantasea's latest housing have been a huge success and very popular, so in the end I think it's a question of budget. If you can afford to get both the Nauticam housing & wide angle lens, go for that, otherwise, get the Fantasea + wide angle.
Here's a short comparison of all the options:
Sony RX100 III - Underwater Housings Comparison