Is applying for a PhD at Oxbridge particularly competitive (compared to other unis)

I am shortlisting PhDs to apply to purely by topic area and coincidentally the ones I am most interested in are at Oxbridge. I feel really intimidated and am thinking of not applying because I don't think I would be a competitive applicant. However, I know PhDs in general are competitive no matter what university. I went to pretty average universities for undergraduate and master's but I did well grade-wise (first and distinction). However I think for that reason I don't feel like Oxbridge material.

At PhD level, does the prestige of Oxbridge matter? Please don't worry about offending me, I would rather hear honest opinions.

It's the quality of your previous academic work, plus the strength of your research proposal, combined with the fit with a Supervisor that counts. Have Oxford and Cambridge both got academics that are a very close fit to what you want to research?

When you say quality of previous academic work, are you referring to just grades?
My subject area is biology so it is specific PhD projects I will be applying for, and yes the ones at Oxford and Cambridge align really well with my research interests and my master's project.
Edit: Also because it's in Biology I don't submit a research proposal but just a personal statement.