As none of the previous Princesses Royal were peeresses in their own right, and there is no other truly comparable situation, I don't think it is possible to know which title would take precedence if a Princess Royal were also granted a peerage.
Interesting. Could you please share the link to those interviews?
Princess Anne was apparently given the option of noble titles for her children:
https://www.nytimes.com/1977/11/16/...irth-to-boy-fifth-in-line-to-the-british.html
"In a departure from tradition, the child will not be given a title. [...] Many Britons were surprised when Buckingham Palace confirmed the decision a few days ago. No reason was given but it was speculated that the young parents, both of whom are known as freewheeling and independent, did not want peerages for themselves or their children."
BBC ON THIS DAY | 15 | 1977: Princess Anne gives birth to Master Phillips
"Both the princess and her husband are said to have rejected an offer from the Queen of titles which would have enabled their children to be born into the peerage."
https://www.nowtolove.co.nz/celebrity/royals/zara-tindall-i-dont-think-of-myself-as-royal-40353
Zara Tindall: "My parents didn't give me or my brother titles, so we've been able to have a slightly more normal upbringing.
"As soon as you have got a title, it is very difficult to shed it. I'm very lucky that both my parents decided not to use the title. We grew up and did all the things that gave us the chance to do."