I don't have a tap extractor - but it seemed like a good idea, so I starting reading up and watching Youtube's after reading your post. I figure I might want to have a set on hand too.
I presume you're debating between this version with fixed "fingers" and the Walton with extendable fingers and a outer sliding collar.
From the complaints I read and the Youtube videos of people demonstrating how to break the Walton tap extractors, it seems like a critical factor is how close you can get the collar to the work surface. I.e. my theory is that if you leave it farther from where the tap enters the hole, the fingers flex as you apply force and are more likely to snap. If you can choke up close, you can rely more on the shear strength of those fingers.
That's my armchair guess anyway.
How that relates to the two different styles is that, with the version with the fixed fingers, if you cannot drive them deep enough into the hole so the solid part bottoms out, presumably they can flex and break easily. If you can drive it in all the way, they're probably not much different from the Walton (at least in design - I've no idea of the metallurgy).
I'm tempted to try the cheap ones myself since, if I can't get the tap out that way, I probably need a different solution anyway,
By the way, in the past when I've broken a tap and there's nothing outside the hole to grab, I've used a punch to break pieces off. It's a royal pain, but can work.