If you're looking into modern auto-censoring apps, you will probably have seen a few names being thrown around: Beta Safety, Beta Protection, Beta Suite and PuryFi. There's a whole comparison for Beta Safety available here, and a comparison for Beta Suite available here but this page is intended to deliver a brief summary of how Beta Protection and PuryFi compare.
To be clear, neither option is inherenly better than the other. PuryFi is a great bit of software and if it meets your needs, use it! This won't try and change your mind, just give you an idea of where each software's strengths lie. There's three major points of difference and then a handful of smaller (but still noticeable) differences.
Browser Choice
Here's one of the two big ones: PuryFi only supports Firefox, Beta Protection only supports all the Chrome-based browsers (Chrome, Edge, Opera, Vivaldi, etc). If you'd prefer to stick with your current browser, then pick the extension that supports that browser.
Backend (or lack thereof)
Beta Protection (like Beta Suite and Beta Safety before it) splits the censoring process into two parts: the browser extension (Beta Protection) and a compatible censoring backend (generally Beta Censoring or Beta Safety). That means you need to run the censoring backend separately and the extension in your browser will communicate seamlessly with the backend to do the actual censoring. On the other hand, PuryFi is completely self-contained so all the censoring happens inside your browser.
Obviously that makes PuryFi a noticeably simpler setup and it can be more performant depending on your PC and browser setup. Conversely, especially for advanced users, it means you can't "offload" the hard work of censoring to a different PC, or independently use the censoring backend outside of your browser.
Paywalls, Features and Transparency
PuryFi has features that Beta Protection simply doesn't have. One of the most noticeable is video/GIF support, but that is locked behind a paywall. You need to pay to gain access to a decent chunk of PuryFi's features. Beta Protection is completely free and always will be. There are no features locked behind a paywall, everything is available from the get-go and there is not even any license/account system of any kind in Beta Protection.
Additionally, PuryFi is proprietary and closed source. That means you cannot (easily) check the source code of PuryFi, nor can you validate any claims around its privacy or functionality. To be clear, I have not seen any evidence of any foul play or even suspicious behaviour but you are having to take that largely on faith as PuryFi do not provide their source code, nor do they openly provide their AI model or any of the infrastructure they use. They don't even publish public release notes without payment.
Beta Protection and Beta Censoring are both completely open source, so you can always check anything yourself or even customize it to your liking if you want.
Completely local
This is a more minor point, but we think it's worth drawing attention to: Beta Protection and Beta Censoring are designed to be completely standalone. There's no "phone-home", no connections back to any central services of any kind. Not only does this give you more privacy, it also means that Beta Protection will stay completely functional, no matter if it stops being maintained or any links go offline etc.
Features
As mentioned, PuryFi has some features that Beta Protection simply doesn't have, and some of which it likely never will have. That being said, Beta Protection also has a few features that PuryFi doesn't. One of the most popular that PuryFi does not have (at the time of writing) is overrides, which allows your Beta Protection preferences to be locked in place by yourself or another user, preventing changes and locking you in to a particular censoring experience. Apparently, this is in progress from PuryFi, but it's already available in a completely local privacy-respecting fashion in Beta Protection today. Likewise, as far as I have seen, Puryfi doesn't currently support batch censoring images from your PC (not on a webpage), something Beta Protection supports natively.
Other Differences
There's almost certainly a lot of other differences here, but I have extremely limited experience with PuryFi as I don't agree with either closed source software, or with paywalled features, both of which are endemic to the PuryFi experience. That is obviously a decision every user should individually make, and neither outcome is incorrect.
If there's one thing I'd stress, it's to please refrain from getting bogged down in comparisons/disagreements around the myriad of software options available for this kink. Find what works for you, make the most of it, and give back to the community if you can.