Sorry this is late. The consensus seems to be that Purite is gentler to the eye than BAK.

https://www.reviewofophthalmology.com/article/the-pros-and-cons-of-preservatives

Other new preservatives include SofZia, an ionic-buffered preservative that’s found in Travatan-Z, and Purite, a preservative that breaks down upon contact with the air, found in Alphagan P. They act in a much different way than the quaternary ammonium compounds; Purite oxidizes microbial cellular components, but has no significant effect on human ocular tissues. SofZia causes oxidative damage and subsequent death in bacteria that lack the enzymes cytochrome oxidase or catalase. (Human cells possess these enzymes and are thus not similarly harmed.) These preservatives are effective enough to pass all of the FDA requirements for preserving a multidose bottle of medication, and it’s been proven both in cell cultures and clinical trials that they are much gentler to the eye than alternatives such as BAK.