I advocate for a mixed approach. In my thesis acknowledgements, each individual was initially introduced in the third person, essentially for the reasons Daniel Wessel has mentioned above. The goal is for the Acknowledgements section to be read by more people than just the ones you are acknowledging.
However, for a proper subset of the acknowledged individuals, namely those I wanted to highlight, I included short personal messages in the second person. The goal was to highlight these individuals, break the monotony of just listing names, and inject something personal and heartfelt into the text.
Here is an example:
I am deeply indebted to Professor Dumbledore for his constant and genuine
support of all his students. I would not be where I am today without
him. Albus, I miss you every day.
The actual acknowledgements I wrote can be found on my website (within my thesis) if you're interested.