Hi Maurillo, I have been on each of them twice. I think the Mermaid 1 is a bit better. But I don't know about the budget cabins on the Mermaid 1. The cabins on the Aurora are all below deck. The Mermaid 1 is a metal boat, no sails. The Aurora is a wooden phinisi type boat with sails - they always use their motor, but may unfurl their sails on the last day for photos which is very picturesque.
On the Mermaid 1, the crew was very good and knowledgeable both times. On the Aurora, once very good and knowledgeable, and once good. Food was very good on both boats, maybe better on the Mermaid 1. The diving deck set up on the Mermaid 1 is better. The guests on the Aurora tend to be mostly Italian (Italian owned boat, I was told). The Mermaid guests tend to be from all over.
Hope this helps.